Exhibit 99.4

YOUR VOTE IS IMPORTANT! PLEASE VOTE BY: P.O. BOX 8016, CARY, NC 27512-9903 TCR2 Therapeutics Inc. Special Meeting of Stockholders For Stockholders as of April 10, 2023 TIME: Tuesday, May 30, 2023 8:00 AM, Eastern Time PLACE: Special Meeting to be held live via the Internet - please visit www.proxydocs.com/TCRR for more details. This proxy is being solicited on behalf of the Board of Directors The undersigned hereby appoints Garry Menzel and Eric Sullivan (the “Named Proxies”), and each or either of them, as the true and lawful attorneys of the undersigned, with full power of substitution and revocation, and authorizes them, and each of them, to vote all the shares of common stock of TCR2 Therapeutics Inc. which the undersigned is entitled to vote at said meeting and any adjournment or postponement thereof upon the matters specified and upon such other matters as may be properly brought before the meeting or any adjournment or postponement thereof, conferring authority upon such true and lawful attorneys to vote in their discretion on such other matters as may properly come before the meeting and revoking any proxy heretofore given. THE SHARES REPRESENTED BY THIS PROXY WILL BE VOTED AS DIRECTED OR, IF NO DIRECTION IS GIVEN, SHARES WILL BE VOTED FOR PROPOSAL 1 AND FOR PROPOSAL 2. THE PROXIES WILL VOTE IN THEIR DISCRETION ON ANY OTHER BUSINESS AS MAY PROPERLY COME BEFORE THE MEETING AND ANY ADJOURNMENT OR POSTPONEMENT THEREOF. You are encouraged to specify your choice by marking the appropriate box (SEE REVERSE SIDE) but you need not mark any box if you wish to vote in accordance with the Board of Directors’ recommendation. The Named Proxies cannot vote your shares unless you sign (on the reverse side) and return this card. PLEASE BE SURE TO SIGN AND DATE THIS PROXY CARD AND MARK ON THE REVERSE SIDE INTERNET Go To: www.proxypush.com/TCRR • Cast your vote online • Have your Proxy Card ready • Follow the simple instructionsto record your vote PHONE Call 1-844-925-2423 • Use any touch-tone telephone • Have your Proxy Card ready • Follow the simple recorded instructions MAIL • Mark,sign and date your Proxy Card • Fold and return your Proxy Card in the postage-paid envelope provided “ALEXA, VOTE MY PROXY” • Open Alexa app and browse skills • Search “Vote my Proxy” • Enable skill TO ATTEND the Special Meeting, please visit www.proxydocs.com/TCRR for virtual meeting registration details.

TCR2 Therapeutics Inc. Special Meeting of Stockholders Please make your marks like this: The Board of Directors Recommends a Vote FOR Proposal 1 and FOR Proposal 2. PROPOSAL YOUR VOTE 1. To adopt the Agreement and Plan of Merger, dated March 5, 2023 (as it may be amended from time to time), by and among TCR2 Therapeutics Inc., Adaptimmune Therapeutics plc and CM Merger Sub, Inc. (the “merger proposal”) BOARD OF DIRECTORS RECOMMENDS 2. To approve the adjournment or postponement of the TCR2 special meeting, if necessary or appropriate, to solicit additional proxies if there are not sufficient votes at the time of the TCR2 special meeting to approve the merger proposal or to ensure that any supplement or amendment to this joint proxy statement/prospectus is timely provided to TCR2 stockholders FOR TO ATTEND the Special Meeting, please visit www.proxydocs.com/TCRR for virtual meeting registration details. Authorized Signatures- Must be completed for your instructions to be executed. Please sign exactly as your name(s) appears on your account. If held in joint tenancy, all persons should sign. Trustees, administrators, etc., should include title and authority. Corporations should provide full name of corporation and title of authorized officer signing the Proxy/Vote Form. Signature (and Title if applicable) Date Signature (if held jointly) Date FOR FOR AGAINST ABSTAIN FOR AGAINST ABSTAIN X