Exhibit (12)(a)

Chicago New York Washington, DC London San Francisco Los Angeles Singapore

November 18, 2019

Nuveen AMT-Free Quality Municipal Income Fund

333 West Wacker Drive

Chicago, Illinois 60606

Nuveen North Carolina Quality Municipal Income Fund

333 West Wacker Drive

Chicago, Illinois 60606

Re: Reorganization of Nuveen North Carolina Quality Municipal Income Fund into Nuveen AMT-Free Quality Municipal Income Fund

Ladies and Gentlemen:

You have requested our opinion regarding certain U.S. federal income tax consequences of the reorganization (the “Reorganization”) by and between Nuveen North Carolina Quality Municipal Income Fund, a Massachusetts business trust (the “Target Fund”), and Nuveen AMT-Free Quality Municipal Income Fund, a Massachusetts business trust (the “Acquiring Fund”). The Target Fund and the Acquiring Fund are each referred to herein as a “Fund” and collectively, as the “Funds.”

The Reorganization contemplates the transfer of substantially all the assets of the Target Fund to the Acquiring Fund solely in exchange for (i) voting common shares of beneficial interest, par value $0.01 per share, of the Acquiring Fund (“Acquiring Fund Common Shares”), (ii) voting Adjustable Rate MuniFund Term Preferred Shares (“AMTP Shares”), Series 2028, par value $0.01 per share and liquidation preference $100,000 per share, of the Acquiring Fund having all the various rights, preferences and privileges set forth in the Statement Establishing and Fixing the Rights and Preferences of Adjustable Rate MuniFund Term Preferred Shares, Series 2028 (“Acquiring Fund AMTP Shares” and together with Acquiring Fund Common Shares, the “Acquiring Fund Shares”), and (iii) the assumption by the Acquiring Fund of substantially all the liabilities of the Target Fund. As part of the Reorganization, the Target Fund will immediately thereafter distribute to its shareholders of record all the Acquiring Fund Shares so received in complete liquidation of the Target Fund, and the Target Fund promptly thereafter will be dissolved under applicable state law. The foregoing will be accomplished pursuant to an Agreement and Plan of Reorganization, dated as of July 26, 2019 (the “Plan”), entered into by the Target Fund and the Acquiring Fund.

In rendering this opinion, we have examined the Plan and have reviewed and relied upon (i) representations made to us by duly authorized officers of the Funds in letters dated November 18, 2019 (collectively, the “Representation Letters”) and (ii) the opinion of Stradley Ronon Stevens & Young, LLP dated November 18, 2019 regarding the Acquiring Fund AMTP Shares issued in the Reorganization being treated as equity for federal income tax purposes (the “Equity Opinion”). We have also examined such other agreements, documents, corporate records and other materials as we have deemed necessary in order for us to render the opinions referred to in this letter. In such review and examination, we have assumed the genuineness of all signatures, the legal capacity and authority of the parties who executed such documents, the authenticity of all documents submitted to us as originals, the conformity to originals of all documents submitted to us as copies and the authenticity of the originals of such latter documents.

222 North LaSalle Street | Chicago, Illinois 60601 | T +1 312 609 7500 | F +1 312 609 5005

Vedder Price P.C. is affiliated with Vedder Price LLP, which operates in England and Wales, Vedder Price (CA), LLP, which operates in California, and Vedder Price Pte. Ltd., which operates in Singapore.

Nuveen AMT-Free Quality Municipal Income Fund

Nuveen North Carolina Quality Municipal Income Fund

November 18, 2019

Page 2

Our opinion is based, in part, on the assumptions that (i) the Reorganization described herein will occur in accordance with the terms of the Plan (without the waiver or modification of any terms or conditions thereof and without taking into account any amendment thereof that we have not approved) and the facts and representations set forth or referred to in this opinion letter, and that such facts and representations, as well as the facts and representations set forth in the Plan, are true, correct and complete as of the date hereof and will be true, correct and complete as of the date and time of the Closing (as defined in the Plan) (the “Effective Time”), (ii) any representation set forth in the Representation Letters qualified by knowledge, intention, belief or any similar qualification are, and will be as of the Effective Time, true, correct and complete without such qualification, and (iii) the Acquiring Fund AMTP Shares issued in the Reorganization will be treated as stock of the Acquiring Fund for federal income tax purposes, which assumption is consistent with the Equity Opinion. You have not requested that we undertake, and we have not undertaken, any independent investigation of the accuracy of the facts, representations and assumptions set forth or referred to herein.

For the purposes indicated above, and based upon the facts, assumptions and representations set forth or referred to herein, it is our opinion that for U.S. federal income tax purposes:

1.    The transfer by the Target Fund of substantially all its assets to the Acquiring Fund solely in exchange for Acquiring Fund Shares and the assumption by the Acquiring Fund of substantially all the liabilities of the Target Fund, immediately followed by the distribution of all the Acquiring Fund Shares so received by the Target Fund to the Target Fund’s shareholders of record in complete liquidation of the Target Fund and the dissolution of the Target Fund promptly thereafter, will constitute a “reorganization” within the meaning of section 368(a)(1) of the Internal Revenue Code of 1986, as amended (the “Code”), and the Acquiring Fund and the Target Fund will each be a “party to a reorganization,” within the meaning of section 368(b) of the Code, with respect to the Reorganization.

2.    No gain or loss will be recognized by the Acquiring Fund upon the receipt of substantially all the Target Fund’s assets solely in exchange for Acquiring Fund Shares and the assumption by the Acquiring Fund of substantially all the liabilities of the Target Fund. (Section 1032(a) of the Code).

3.    No gain or loss will be recognized by the Target Fund upon the transfer of substantially all its assets to the Acquiring Fund solely in exchange for Acquiring Fund Shares and the assumption by the Acquiring Fund of substantially all the liabilities of the Target Fund or upon the distribution (whether actual or constructive) of such Acquiring Fund Shares to the Target Fund’s shareholders solely in exchange for such shareholders’ shares of the Target Fund in complete liquidation of the Target Fund. (Sections 361(a) and (c) and 357(a) of the Code).

4.    No gain or loss will be recognized by the Target Fund’s shareholders upon the exchange, pursuant to the Plan, of all their shares of the Target Fund solely for Acquiring Fund Shares, except to the extent the Target Fund’s common shareholders receive cash in lieu of a fractional Acquiring Fund Common Share. (Section 354(a) of the Code).

Nuveen AMT-Free Quality Municipal Income Fund

Nuveen North Carolina Quality Municipal Income Fund

November 18, 2019

Page 3

5.    The aggregate basis of the Acquiring Fund Shares received by each Target Fund shareholder pursuant to the Reorganization (including any fractional Acquiring Fund Common Share to which a shareholder would be entitled) will be the same as the aggregate basis of the Target Fund shares exchanged therefor by such shareholder. (Section 358(a)(1) of the Code).

6.    The holding period of the Acquiring Fund Shares received by each Target Fund shareholder in the Reorganization (including any fractional Acquiring Fund Common Share to which a shareholder would be entitled) will include the period during which the shares of the Target Fund exchanged therefor were held by such shareholder, provided such Target Fund shares were held as capital assets at the Effective Time. (Section 1223(1) of the Code).

7.    The basis of the assets of the Target Fund received by the Acquiring Fund will be the same as the basis of such assets in the hands of the Target Fund immediately before the Effective Time. (Section 362(b) of the Code).

8.    The holding period of the assets of the Target Fund received by the Acquiring Fund will include the period during which such assets were held by the Target Fund. (Section 1223(2) of the Code).

Notwithstanding anything to the contrary herein, we express no opinion as to the effect of the Reorganization on the Target Fund, the Acquiring Fund or any Target Fund shareholder with respect to any asset (including without limitation any stock held in a passive foreign investment company as defined in section 1297(a) of the Code) as to which any unrealized gain or loss is required to be recognized under federal income tax principles (i) at the end of a taxable year or upon the termination thereof, or (ii) upon the transfer of such asset regardless of whether such transfer would otherwise be a non-taxable transaction under the Code.

FACTS

Our opinion is based upon the facts, representations and assumptions set forth or referred to above and the following facts and assumptions, any alteration of which could adversely affect our conclusions.

The Target Fund has been registered and operated, since it commenced operations, as a closed-end management investment company under the Investment Company Act of 1940, as amended (the “1940 Act”). The Target Fund’s common shares are listed and traded on the New York Stock Exchange (“NYSE”) under the symbol NNC. The Target Fund currently has outstanding AMTP Shares, Series 2028. All the outstanding common shares and AMTP Shares of the Target Fund are treated as equity for federal income tax purposes. The Target Fund is treated as a corporation for federal income tax purposes, has elected to be taxed as a regulated investment company under section 851 of the Code for all its taxable years, including without limitation the taxable year in which the Reorganization occurs, and has qualified and will continue to qualify for the tax treatment afforded regulated investment companies under the Code for each of its taxable years, including without limitation the taxable year in which the Reorganization occurs.

The Acquiring Fund similarly has been registered and operated since it commenced operations as a closed-end management investment company under the 1940 Act. The Acquiring Fund Common Shares are listed and traded on the NYSE under the symbol NEA. In addition, the Acquiring Fund currently has

Nuveen AMT-Free Quality Municipal Income Fund

Nuveen North Carolina Quality Municipal Income Fund

November 18, 2019

Page 4

outstanding five series of Variable Rate Demand Preferred Shares and four series of MuniFund Preferred Shares. As part of the Reorganization, the Acquiring Fund will issue one new series of Acquiring Fund AMTP Shares, Series 2028. The Acquiring Fund Common Shares and Acquiring Fund AMTP Shares to be issued in the Reorganization will be treated as equity for federal income tax purposes. The Acquiring Fund is treated as a corporation for federal income tax purposes, has elected to be taxed as a regulated investment company under section 851 of the Code for all its taxable years, including without limitation the taxable year in which the Reorganization occurs, and has qualified and will continue to qualify for the tax treatment afforded regulated investment companies under the Code for each of its taxable years, including without limitation the taxable year in which the Reorganization occurs.

Upon satisfaction of certain terms and conditions set forth in the Plan on or before the Effective Time, the Acquiring Fund will acquire substantially all the assets of the Target Fund solely in exchange for newly issued Acquiring Fund Shares and the assumption by the Acquiring Fund of substantially all the liabilities of the Target Fund. Immediately thereafter, the Target Fund will distribute to its shareholders of record all the Acquiring Fund Shares so received in complete liquidation of the Target Fund, and promptly thereafter, the Target Fund will be dissolved under applicable state law. The assets of the Target Fund to be acquired by the Acquiring Fund will include, without limitation, cash, securities, commodities, interests in futures, dividends or interest receivables owned by the Target Fund and any deferred or prepaid expenses shown as an asset on the books of the Target Fund as of the Closing. The Target Fund will retain assets sufficient to pay all accumulated and unpaid dividends on all outstanding AMTP Shares of the Target Fund and all declared but unpaid dividends on all outstanding common shares of the Target Fund. In the Reorganization, the Acquiring Fund will acquire at least ninety percent (90%) of the fair market value of the Target Fund’s net assets and at least seventy percent (70%) of the fair market value of the Target Fund’s gross assets held immediately prior to the Reorganization.

The Acquiring Fund Common Shares issued to the Target Fund will have the same aggregate net asset value, as of the Valuation Time (as defined in the Plan), as the aggregate value of the net assets of the Target Fund transferred to the Acquiring Fund (net of the liquidation preference of all the outstanding AMTP Shares of the Target Fund) as of such time. The number of Acquiring Fund AMTP Shares issued to the Target Fund will be equal to the number of Target Fund AMTP Shares, Series 2028, outstanding immediately prior to the Reorganization and shall consist solely of Acquiring Fund AMTP Shares, Series 2028. The Acquiring Fund AMTP Shares issued to the Target Fund will have the same liquidation preference and substantially similar terms as the AMTP Shares of the Target Fund outstanding at the Effective Time.

Immediately after the Effective Time, the Target Fund will be liquidated and will distribute the newly issued Acquiring Fund Common Shares it received pro rata to its common shareholders of record in exchange for such shareholders’ Target Fund common shares and will distribute one Acquiring Fund AMTP Share, Series 2028, to its AMTP shareholders of record for each Target Fund AMTP Share, Series 2028, held by such shareholder. In such distribution, Acquiring Fund AMTP Shares shall be distributed only to holders of, and in exchange for, AMTP Shares of the Target Fund. No fractional Acquiring Fund Common Shares will be issued in connection with the Reorganization. In lieu thereof, the Acquiring Fund’s transfer agent, on behalf of the shareholders entitled to receive fractional Acquiring Fund Common Shares, will aggregate all fractional Acquiring Fund Common Shares and sell the resulting whole shares on the NYSE for the account of all shareholders of fractional interests, and each such shareholder will be entitled to a pro rata share of the proceeds from such sale.

Nuveen AMT-Free Quality Municipal Income Fund

Nuveen North Carolina Quality Municipal Income Fund

November 18, 2019

Page 5

As a result of the Reorganization, every common shareholder of the Target Fund will own Acquiring Fund Common Shares (including for this purpose any fractional shares to which they would be entitled) that will have an aggregate per share net asset value as of the Valuation Time equal to the aggregate per share net asset value of the Target Fund common shares held by such shareholder as of the Valuation Time and each holder of Target Fund AMTP Shares will own Acquiring Fund AMTP Shares with an aggregate liquidation preference and value as of the Effective Time equal to the aggregate liquidation preference and value of the Target Fund AMTP Shares held by such shareholder as of the Effective Time.

Following the Reorganization, the Acquiring Fund will continue the Target Fund’s historic business in that it will have a similar investment objective and similar investment strategies, policies, risks and restrictions as those of the Target Fund. In addition, the Acquiring Fund will use a significant portion of the Target Fund’s historic business assets in its business. At the Effective Time, at least thirty-four percent (34%) of the total fair market value of the Target Fund’s portfolio assets will meet the investment objective, strategies, policies, risks and restrictions of the Acquiring Fund. The Target Fund will not have altered its portfolio in connection with the Reorganization to meet this thirty-four percent (34%) threshold. Neither Fund modified any of its investment objective, strategies, policies, risks or restrictions in connection with the Reorganization and the Acquiring Fund has no plan or intention to change any of its investment objective, strategies, policies, risks or restrictions after the Reorganization.

In approving the Reorganization, the Board of Trustees of each Fund (the “Boards”) determined that the Plan and the transactions contemplated thereunder are in the best interests of its Fund and that the interests of the shareholders of its Fund will not be diluted as a result of the Reorganization. In making such determination, the Boards considered that the Reorganization may result in operating efficiencies as a result of the larger net asset size of the Acquiring Fund following the Reorganization.

CONCLUSION

Based on the foregoing, it is our opinion that the transfer of substantially all the assets of the Target Fund, pursuant to the Plan, to the Acquiring Fund solely in exchange for Acquiring Fund Shares and the assumption by the Acquiring Fund of substantially all the liabilities of the Target Fund followed by the complete liquidation of the Target Fund immediately thereafter and the dissolution of the Target Fund promptly thereafter will qualify as a reorganization under section 368(a)(1) of the Code.

The opinions set forth above (subject to the limitations set forth above) with respect to (i) the nonrecognition of gain or loss by the Target Fund and the Acquiring Fund, (ii) the basis and holding period of the assets received by the Acquiring Fund, (iii) the nonrecognition of gain or loss by the Target Fund’s shareholders upon the receipt of the Acquiring Fund Shares, except with respect to cash received in lieu of a fractional Acquiring Fund Common Share, and (iv) the basis and holding period of the Acquiring Fund Shares received by the Target Fund’s shareholders follow as a matter of law from the opinion that the transfers under the Plan will qualify as a reorganization under section 368(a)(1) of the Code.

The opinions expressed in this letter are based on the Code, the Income Tax Regulations promulgated by the Treasury Department thereunder and judicial authority reported as of the date hereof. We have also considered the positions of the Internal Revenue Service (the “Service”) reflected in published and private rulings. Although we are not aware of any pending changes to these authorities that would alter our opinions, there can be no assurances that future legislative or administrative changes, court decisions or Service interpretations will not significantly modify the statements or opinions expressed herein. We do not undertake to make any continuing analysis of the facts or relevant law following the date of this letter or to notify you of any changes to such facts or law.

Nuveen AMT-Free Quality Municipal Income Fund

Nuveen North Carolina Quality Municipal Income Fund

November 18, 2019

Page 6

Our opinion is limited to those U.S. federal income tax issues specifically considered herein. We do not express any opinion as to any other federal tax issues, or any state, local or foreign tax law issues, arising from or related to the transactions contemplated by the Plan.

Although the discussion herein is based upon our best interpretation of existing sources of law and expresses what we believe a court would properly conclude if presented with these issues, no assurance can be given that such interpretations would be followed if they were to become the subject of judicial or administrative proceedings.

This opinion is furnished to the Funds solely for their benefit in connection with the Reorganization and is not to be relied upon, quoted, circulated, published, or otherwise referred to for any other purpose, in whole or in part, without our express prior written consent. This opinion may be disclosed to shareholders of the Funds and they may rely on it, it being understood that we are not establishing any attorney-client relationship with any shareholder of either Fund. This letter is not to be relied upon for the benefit of any other person.

We hereby consent to the filing of a form of this opinion as an exhibit to the Registration Statement on Form N-14 (File No. 333-232029) relating to the Reorganization filed by the Acquiring Fund with the Securities and Exchange Commission (the “Registration Statement”); to the discussion of this opinion in the Joint Proxy Statement/Prospectus dated August 2, 2019 relating to the Registration Statement; and to the use of our name and to any reference to our firm in the Registration Statement, in the Proxy Statement for holders of AMTP Shares of the Target Fund and in the Confidential Information Memorandum relating to the Acquiring Fund AMTP Shares. In giving such consent, we do not thereby admit that we are within the category of persons whose consent is required under section 7 of the Securities Act of 1933, as amended, or the rules and regulations of the Securities and Exchange Commission thereunder.

Very truly yours,

/s/ Vedder Price P.C.

VEDDER PRICE P.C.