Exhibit 32.1

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Section 906 Certificate

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Certification Pursuant to 18 U.S.C. Section 1350, as Adopted Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002

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Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (subsections (a) and (b) of Section 1350, Chapter 63 of Title 18, United States Code), I, Adrian Rawcliffe, Chief Executive Officer of Adaptimmune Therapeutics plc, a public limited company incorporated under English law (the “Company”), hereby certify, to my knowledge, that:

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1.        The Company’s Quarterly Report on Form 10-Q for the quarterly period ended June 30, 2021, to which this Certification is attached as Exhibit 32.1 (the “Quarterly Report”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

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2.        The information contained in the Quarterly Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

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Date: August 9, 2021

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