Exhibit 10.1

September 27, 2024

Evoke Pharma, Inc.

420 Stevens Avenue, Suite 230

Solana Beach, CA 92075

Re: Warrant Amendments, dated September 27, 2024, to those certain Series A Common Stock Purchase Warrants and Series C Common Stock Purchase Warrants

Ladies and Gentlemen:

Reference is made to those certain Warrant Amendments, dated September 27, 2024 (the “Warrant Amendments”), by and between Evoke Pharma, Inc. (the “Company”) and each of Nantahala Capital Partners Limited Partnership, NCP RFM LP and Blackwell Partners LLC, affiliates of Nanthala Capital Management, LLC (“Nantahala Capital Management”). Capitalized terms used but not otherwise defined herein shall have the meanings given to such terms in the Warrant Amendments.

The Company agrees that (i) for as long as Nantahala Capital Management, or its affiliates (“Nantahala”) beneficially own securities representing at least 5% of the ordinary voting power of all common stock of the Company, par value $0.0001 per share, then outstanding (“Common Stock”), Nantahala shall have the right, subject to compliance with applicable Nasdaq rules, to designate one (1) member of the board of directors of the Company and (ii) for as long as Nantahala beneficially own securities representing at least 15% of the ordinary voting power of all Common Stock, Nantahala shall have the right, subject to compliance with applicable Nasdaq rules, to designate two (2) members of the board of directors of the Company (each designee, a “Nantahala Board Representative”).

For as long as Nantahala holds the right to designate aNantahala Board Representative pursuant to this letter agreement, the Company shall cause such Nantahala Board Representative to be elected or appointed to the board of directors, including by taking all action as may be necessary to secure the favorable votes of the board of directors or the stockholders of the Company, as applicable, in respect of the election or appointment of such Nantahala Board Representative at the time of any future director elections or appointments (including to fill any vacancy), whether at any annual or special meeting of the board of directors or stockholders or pursuant to any written consent of the board of directors or stockholders of the Company or, to the extent necessary, by expanding the size of the board of directors or seeking the resignation of a member of the board of directors as of the date hereof, and appointing the Nantahala Board Representative to the board of directors (and, to the extent necessary, calling a special meeting of the Company’s stockholders for the purpose of amending the Company’s certificate of incorporation, bylaws and other governing documents, as required to allow such expansion). As soon as practicable following the designation of a Nantahala Board Representative by Nantahala, the Company shall cause such person to be elected or appointed to the board of directors as a Nantahala Board Representative.

For as long as Nantahala holds the right to designate a member of the board of directors pursuant to this letter agreement, the Company shall not, without the prior written approval of the Nantahala Board Representative:

(i)             increase the size of the board of directors in excess of six (6) members plus that number of directors that Nantahala has the right to designate pursuant to this letter agreement; or

(ii)            decrease the size of the board of directors if such decrease would require the resignation from the board of directors of a Nantahala Board Representative then serving as a member of the board of directors.

The Company will reimburse the Nantahala Board Representatives then serving as members of the board of directors for their reasonable and documented out-of-pocket expenses incurred in connection with travel to or from and attendance at each meeting of the board of directors. The Nantahala Board Representatives then serving as members of the board of directors will be entitled to compensation by the Company in accordance with the Company’s standard compensation policies as in effect from time to time.

For as long as Nantahala holds the right to designate a member of the board of directors pursuant to this letter agreement, in the event that a vacancy is created at any time by the death, disability, retirement, resignation or removal of a Nantahala Board Representative, Nantahala may designate another individual to be elected to fill the vacancy created thereby, and the Company hereby agrees to take, at any time and from time to time, all actions necessary to accomplish the same.

If the Company reasonably determines that a Nantahala Board Representative is subject to any of the “bad actor” disqualifications (“Disqualification Events”) described in Rule 506(d)(1)(i) through (viii) under the Securities Act of 1933, as amended, as evidenced by the written advice of legal counsel of national or international standing, then the Nantahala Board Representative shall not be eligible for appointment to the board of directors. When designating a Nantahala Board Representative, Nantahala will confirm that, to its knowledge, such designee is not subject to a Disqualification Event.

The Nantahala Board Representatives shall be entitled to indemnification by the Company to the maximum extent permitted by applicable law and the Company’s governing documents. the Company shall enter into an indemnification agreement with any Nantahala Board Representative on terms of the Company’s form of indemnification agreement previously provided to Nantahala.

For as long as Nantahala holds the right to designate a member of the board of directors pursuant to this letter agreement, Nantahala shall have the right, subject to compliance with applicable Nasdaq rules, to designate one (1) member of each committee of the board of directors that now exists or may be established pursuant to the Company’s governing documents or by the board of directors from time to time.

If the foregoing correctly sets forth the understanding between the Company and Nantahala, please so indicate in the space provided below for that purpose, whereupon this letter shall constitute a binding agreement between the Company and Nantahala. This letter agreement may be executed by any one or more of the parties hereto in any number of counterparts, each of which shall be deemed to be an original, but all such respective counterparts shall together constitute one and the same instrument. This letter agreement may be delivered by any party by facsimile, email or other electronic transmission.

[Signature Page Follows]

Very truly yours,

EVOKE PHARMA, INC.

By: /s/ Matthew J. D’Onofrio

Name: Matthew J. D’Onofrio

Title: Chief Executive Officer

Acknowledged and agreed:

NANTAHALA CAPITAL MANAGEMENT, LLC

By: /s/ Daniel Mack

Name: Daniel Mack

Title: Manager

[Signature Page to Letter Agreement]