Exhibit (a)(1)(iii)

OFFER BY

CLEARBRIDGE MLP AND MIDSTREAM FUND INC.

TO PURCHASE FOR CASH

UP TO 50% OF THE FUND’S OUTSTANDING

SHARES OF COMMON STOCK

AT 100% OF NET ASSET VALUE PER SHARE

THE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE AT 5:00 P.M.,

NEW YORK CITY TIME, ON JUNE 20, 2024 OR SUCH LATER DATE

TO WHICH THE OFFER IS EXTENDED (“TERMINATION DATE”)

THIS OFFER IS NOT CONDITIONED ON ANY MINIMUM NUMBER OF SHARES BEING

TENDERED, BUT IS SUBJECT TO OTHER CONDITIONS AS OUTLINED IN THE FUND’S

OFFER TO PURCHASE AND IN THE LETTER OF TRANSMITTAL.

May 21, 2024

To  Brokers, Dealers, Commercial Banks,

   Trust Companies and Other Nominees:

We are enclosing herewith the material listed below relating to the offer of ClearBridge MLP and Midstream Fund Inc., a Maryland corporation registered under the Investment Company Act of 1940, as amended, as a closed-end, non-diversified management investment company (the “Fund”), to purchase up to 50% of the Fund’s outstanding shares of common stock (the “Shares”), upon the terms and conditions set forth in its Offer to Purchase dated May 21, 2024 and in the related Letter of Transmittal (which together constitute the “Offer”). The price to be paid for the Shares is an amount per Share, equal to 100% of the net asset value per Share as determined by the Fund at the close of regular trading session on the New York Stock Exchange on June 20, 2024, or if the Offer is extended, on the next trading day after the day to which the Tender Offer is extended.

We are asking you to contact your clients for whom you hold Shares registered in your name (or in the name of your nominee) or who hold Shares registered in their own names. Please bring the Offer to their attention as promptly as possible. No fees or commission will be payable to the Fund in connection with the Offer. However, brokers, dealers or other persons may charge Stockholders a fee for soliciting tenders for Shares pursuant to the Offer. The Fund will also, upon request, reimburse you for reasonable and customary mailing and handling expenses incurred by you in forwarding any of the enclosed materials to your clients. The Fund will pay all transfer taxes on its purchase of Shares, subject to Instruction 6, “Stock Transfer Taxes,” of the Letter of Transmittal. However, backup withholding at a 24% rate may be required unless either an exemption is established or the required taxpayer identification number (in the case of U.S. shareholders) and certifications are provided. In addition, in the case of non-U.S. shareholders, 30% (or lower treaty rate) withholding at the source or under the Foreign Account Tax Compliance Act may be required unless an exemption from or reduction of such withholding is established. See Section 3 of the Offer to Purchase.

For your information and for forwarding to your clients, we are enclosing the following documents:

1. A letter to Stockholders of the Fund from Jane Trust, Chairman, Chief Executive Officer and President of the Fund;

2. The Offer to Purchase, dated May 21, 2024;

3. The Letter of Transmittal for your use and to be provided to your clients;

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Exhibit (a)(1)(iii)

4. Form of letter to clients that may be sent to your clients for whose accounts you hold Shares registered in your name (or in the name of your nominee); and

5. Return envelope addressed to Computershare Inc. and its wholly owned subsidiary, Computershare Trust Company, N.A. (the “Depositary”).

The Offer is not being made to, nor will the Fund accept tenders from, holders of Shares in any state or other jurisdiction in which the Offer would not be in compliance with the securities or Blue Sky laws of such jurisdiction.

None of the Fund, its Board of Directors or the Fund’s investment manager or subadviser makes any recommendation to any Stockholder whether to tender or not to tender any Shares.

Additional copies of the enclosed material may be obtained from the Information Agent at the appropriate address and telephone number set forth in the Fund’s Offer to Purchase. Any questions you have with respect to the Offer should be directed to the Information Agent at its address and telephone numbers set forth in the Offer to Purchase.

Very truly yours,
CLEARBRIDGE MLP AND MIDSTREAM FUND INC.
/s/ Jane Trust
Jane Trust
Chairman, Chief Executive Officer and President

NOTHING CONTAINED HEREIN OR IN THE ENCLOSED DOCUMENTS SHALL MAKE YOU, OR ANY OTHER PERSON, THE AGENT OF THE FUND, THE INFORMATION AGENT, OR THE DEPOSITARY OR AUTHORIZE YOU, OR ANY OTHER PERSON, TO MAKE ANY STATEMENTS OR USE ANY MATERIAL ON THEIR BEHALF WITH RESPECT TO THE OFFER, OTHER THAN THE MATERIAL ENCLOSED HEREWITH AND THE STATEMENTS SPECIFICALLY SET FORTH IN SUCH MATERIAL.

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