Exhibit H

March 4, 2019

CapStar Financial Holdings, Inc.

1201 Demonbreun Street, Suite 700

Nashville, Tennessee 37203

Attn: Robert B. Anderson, Secretary

Re: Notice of Intention to Nominate Board Members for CapStar Financial Holdings, Inc. (the “Company”)

Dear Mr. Anderson:

This letter is in response to your letter, dated February 15, 2019, regarding your purported rejection of my valid nomination of myself and Jason K. West for election to the Board of Directors (the “Board”) of the Company at the 2019 annual meeting of shareholders (the “2019 Annual Meeting”). Your letter stated that my nominations were required to be delivered to the Secretary of the Company between November 19, 2018 and January 3, 2019. Your letter is an admission that the Company’s 2018 Proxy Statement (the “Proxy Statement”) is false and misleading because the dates identified in the Proxy Statement for the nomination of directors at the 2019 Annual Meeting do not match the dates set forth in your letter or as provided in the Company’s Bylaws. As explained in more detail below, the Proxy Statement was false and misleading in violation of Proxy Rules 14a–5 and 14a–9.

Rule 14a–5(e)(2) requires a company to disclose the deadline for submitting a shareholder proposal as established by the advance notice provision in the company’s bylaws. In the Proxy Statement under the heading “How and when may I submit a shareholder proposal for CapStar’s 2019 Annual Meeting of Shareholders?” the Company stated, “Accordingly, a shareholder who intends to raise a proposal to be acted upon at the 2019 Annual Meeting of Shareholders, but who does not desire to include the proposal in the Company’s 2019 definitive proxy statement, must inform the Company by sending written notice to the Company’s Corporate Secretary at CapStar Financial Holdings, Inc., 1201 Demonbreun Street, Suite 700, Nashville, Tennessee 37203, no earlier than December 22, 2017 nor later than February 5, 2018.” (emphasis added). These dates are obviously inconsistent with the November 19, 2018 through January 3, 2019 dates set forth in your letter, in which you reference the Company’s Bylaws. The Company not only failed to disclose the correct deadline for submitting a shareholder proposal, as required by Rule 14a-5(e)(2), but it disclosed false and misleading dates in its Proxy Statement. As a result, the Company violated Rule 14a–5(e)(2) when it set forth an incorrect deadline for shareholder proposals in the Proxy Statement.

The Company also violated Rule 14a–9, which prohibits using a proxy statement containing false or misleading statements as to any material fact. The Company’s use of the February 5 date as the deadline for submitting a shareholder proposal was false and misleading because it did not comport with the Bylaws and gave shareholders the impression that they had an additional month to submit director nominations and shareholder proposals. This deadline was a material fact because it bears directly on the shareholders’ right to nominate directors, which courts have held is an essential component of the shareholders’ fundamental right to vote.

In the Rule 14a–8 shareholder proposal context, the Securities and Exchange Commission (“SEC”) Staff has stated in multiple no-action letters that a company may not omit a shareholder proposal from its proxy statement when the company failed to properly notify its shareholders as to the deadline for submitting proposals. The SEC Staff believes that, when a company has incorrectly identified the date of the deadline in its proxy materials, it is incumbent upon the company to notify the shareholders of the correct date. The SEC Staff does not shift the burden on to shareholders to calculate the correct date. The policy behind the SEC’s Rule 14a–8 guidance would apply equally to the situation in which a company identifies an incorrect deadline under an advance notice bylaw provision. In those situations, a company must notify shareholders of the correct date and cannot shift the burden of calculating the correct date to shareholders. The Company’s rejection of my nomination based on a deadline that the Company erroneously identified is therefore inconsistent with the SEC’s policies.

It is also inconsistent with the principles expressed in judicial decisions. Courts have required boards to waive advance notice requirements if the circumstances so dictate based on equitable principles. This is because courts view the shareholder franchise as sacrosanct and do not look favorably on a board’s attempts to thwart the shareholders’ exercise of the right to vote. Here, the Company’s incumbent directors cannot entrench themselves by purporting to provide extra time for director nominations in a proxy statement, only to later reject nominations that rely on that extended deadline. Under these circumstances, it would be a breach of the fiduciary duties of the Company’s directors to strictly enforce the advance notice provision in its bylaws.

In order to remedy the false and misleading Proxy Statement, the Company must either: a) permit me to nominate myself and Mr. West for election to the Board at the 2019 Annual Meeting pursuant to my prior written request submitted on February 5, 2019; or b) make a filing with the SEC setting forth a revised schedule that would provide shareholders with an opportunity to nominate Board members for inclusion in the Company’s proxy statement for the 2019 Annual Meeting and/or to raise a proposal to be acted on at the 2019 Annual Meeting without inclusion in the proxy statement in accordance with an accurate schedule.

Please inform me of how you intend to remedy your proxy violations by March 11, 2019. Please note that I reserve all rights and remedies with respect to the proxy violations described in this letter.

Sincerely,

/s/ Gaylon M. Lawrence, Jr.

Gaylon M. Lawrence, Jr.

1201 Demonbreun St., Suite 1460

Nashville, TN 37203

(615) 257-7080