Exhibit 10.4

    

    

    

    
      August 6, 2020

       

      ARYA Sciences Acquisition Corp III

      51 Astor Place, 10th Floor

      New York, New York 10003

       

      Re:          Initial Public Offering

       

      Ladies and Gentlemen:

       

      This letter (this “Letter Agreement”) is
        being delivered to you in accordance with the Underwriting Agreement (the “Underwriting Agreement”) entered into by and among ARYA Sciences
        Acquisition Corp III, a Cayman Islands exempted company (the “Company”), Jefferies LLC and Goldman Sachs & Co. LLC, as representatives
        (the “Representatives”) of the several underwriters named therein (the “Underwriters”), relating to an underwritten initial public offering (the “Public Offering”)
        of 14,950,000 of the Company’s Class A ordinary shares, par value $0.0001 per share ( “Ordinary Shares”) (including 1,950,000 Ordinary
        Shares that may be purchased pursuant to the Underwriters’ option to purchase additional Ordinary Shares). The Ordinary Shares will be sold in the Public Offering pursuant to a registration statement on Form S-1 and a prospectus (the “Prospectus”) filed by the Company with the U.S. Securities and Exchange Commission (the “Commission”). Certain capitalized terms used herein are defined in paragraph 1 hereof.

       

      In order to induce the Company and the Underwriters to enter into the Underwriting Agreement and to proceed with the Public Offering and for other good
        and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, ARYA Sciences Holdings III (the “Sponsor”) and
        each of the undersigned (each, an “Insider” and, collectively, the “Insiders”) hereby agree with the Company as follows:

       

      1.           Definitions.
          As used herein, (i) “Business Combination” shall mean a merger,
          share exchange, asset acquisition, share purchase, reorganization or similar business combination with one or more businesses or entities; (ii) “Founder Shares” shall mean the 3,737,500 Class B ordinary shares of the Company, par value $0.0001 per share, outstanding prior to the consummation of the Public
          Offering; (iii) “Private Placement Shares” shall mean the Ordinary
          Shares that will be acquired by the Sponsor for an aggregate purchase price of $4,600,000 (or up to $4,990,000 if the Underwriters’ exercise their option to purchase additional Ordinary Shares in full) in a private placement that shall close
          simultaneously with the consummation of the Public Offering; (iv) “Public Shareholders” shall mean the holders of Ordinary Shares issued in the Public Offering; (v) “Public Shares” shall mean the Ordinary Shares issued in the Public Offering; (vi) “Trust
          Account” shall mean the trust account into which a portion of the net proceeds of the Public Offering and the sale of the Private Placement Shares shall be deposited; (vii) “Transfer” shall mean the (a) sale of, offer to sell, contract or agreement to
          sell, hypothecate, pledge, grant of any option to purchase or otherwise dispose of or agreement to dispose of, directly or indirectly, or establishment or increase of a put equivalent position or liquidation with respect to or decrease of a call
          equivalent position within the meaning of Section 16 of the Securities Exchange Act of 1934, as amended, and the rules and regulations of the Commission promulgated thereunder with respect to, any security, (b) entry into any swap or other
          arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of any security, whether any such transaction is to be settled by delivery of such securities, in cash or otherwise, or (c) public
          announcement of any intention to effect any transaction specified in clause (a) or (b); and (viii) “Charter” shall mean the Company’s Amended and Restated Memorandum and Articles of Association, as the same may be amended from time to time.

       

      
        
          


      

      
      2.            Representations
            and Warranties.

       

      (a)          The Sponsor and each Insider, with
          respect to itself, herself or himself, represent and warrant to the Company that it, she or he has the full right and power, without violating any agreement to which it, she or he is bound (including, without limitation, any non-competition or
          non-solicitation agreement with any employer or former employer), to enter into this Letter Agreement, and, as applicable, to serve as an officer of the Company and/or a director on the Company’s Board of Directors (the “Board”), as applicable, and each Insider hereby consents to being named in the Prospectus, road show and any other materials as an officer and/or director of
          the Company, as applicable.

       

      (b)          Each Insider represents and warrants,
          with respect to herself or himself, that such Insider’s biographical information furnished to the Company (including any such information included in the Prospectus) is true and accurate in all material respects and does not omit any material
          information with respect to such Insider’s background. The Insider’s questionnaire furnished to the Company is true and accurate in all material respects. Each Insider represents and warrants that such Insider is not subject to or a respondent in
          any legal action for, any injunction, cease-and-desist order or order or stipulation to desist or refrain from any act or practice relating to the offering of securities in any jurisdiction; such Insider has never been convicted of, or pleaded
          guilty to, any crime (i) involving fraud, (ii) relating to any financial transaction or handling of funds of another person, or (iii) pertaining to any dealings in any securities and such Insider is not currently a defendant in any such criminal
          proceeding; and such Insider has never been suspended or expelled from membership in any securities or commodities exchange or association or had a securities or commodities license or registration denied, suspended or revoked.

       

      3.           Business
            Combination Vote. It is acknowledged and agreed that the Company shall not enter into a definitive agreement regarding a proposed Business Combination without the prior consent of the Sponsor. The Sponsor and each Insider, with
        respect to itself or herself or himself, agrees that if the Company seeks shareholder approval of a proposed initial Business Combination, then in connection with such proposed initial Business Combination, it, she or he, as applicable, shall vote
        all Founder Shares, Private Placement Shares and any Public Shares held by it, her or him, as applicable, in favor of such proposed initial Business Combination (including any proposals recommended by the Board in connection with such Business
        Combination) and not redeem any Public Shares held by it, her or him, as applicable, in connection with such shareholder approval.

       

      
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      4.           Failure
            to Consummate a Business Combination; Trust Account Waiver.

       

      (a)          The Sponsor and each Insider hereby
          agree, with respect to itself, herself or himself, that in the event that the Company fails to consummate its initial Business Combination within the time period set forth in the Charter, the Sponsor and each Insider shall take all reasonable
          steps to cause the Company to (i) cease all operations except for the purpose of winding up; (ii) as promptly as reasonably possible but not more than 10 business days thereafter, redeem 100% of the Public Shares, at a per-share price, payable in
          cash, equal to the aggregate amount then on deposit in the Trust Account, including interest earned on the funds held in the Trust Account and not previously released to the Company to pay income taxes (less up to $100,000 of interest to pay
          dissolution expenses), divided by the number of then-outstanding Public Shares, which redemption will completely extinguish Public Shareholders’ rights as shareholders (including the right to receive further liquidation distributions, if any);
          and (iii) as promptly as reasonably possible following such redemption, subject to the approval of the Company’s remaining shareholders and the Board, liquidate and dissolve, subject in the case of clauses (ii) and (iii) to the Company’s
          obligations under Cayman Islands law to provide for claims of creditors and in all cases subject to the other requirements of applicable law. The Sponsor and each Insider agree not to propose any amendment to the Charter (i) that would modify the
          substance or timing of the Company’s obligation to provide holders of the Public Shares the right to have their shares redeemed in connection with an initial Business Combination or to redeem 100% of the Public Shares if the Company does not
          complete an initial Business Combination within the required time period set forth in the Charter or (ii) with respect to any provision relating to the rights of holders of Public Shares unless the Company provides its Public Shareholders with
          the opportunity to redeem their Public Shares upon approval of any such amendment at a per-share price, payable in cash, equal to the aggregate amount then on deposit in the Trust Account, including interest earned on the funds held in the Trust
          Account and not previously released to the Company to pay income taxes, if any, divided by the number of then-outstanding Public Shares.

       

      (b)          The Sponsor and each Insider, with
          respect to itself, herself or himself, acknowledges that it, she or he has no right, title, interest or claim of any kind in or to any monies held in the Trust Account or any other asset of the Company as a result of any liquidation of the
          Company with respect to the Founder Shares and Private Placement Shares held by it, her or him, if any. The Sponsor and each  Insider hereby further waives, with respect to any Founder Shares, Private Placement Shares and Public Shares held by
          it, her or him, as applicable, any redemption rights it, she or he may have in connection with (x) the completion of  of the Company’s initial Business Combination,  and (y) a shareholder vote to approve an amendment to the Charter (i) that would
          modify the substance or timing of the Company’s obligation to provide holders of the Public Shares the right to have their shares redeemed in connection with an initial Business Combination or to redeem 100% of the Public Shares if the Company
          has not consummated an initial Business Combination within the time period set forth in the Charter or (ii) with respect to any provision relating to the rights of holders of Public Shares (although the Sponsor and the Insiders shall be entitled
          to liquidation rights with respect to any Public Shares they hold if the Company fails to consummate a Business Combination within the required time period set forth in the Charter).

       

      
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      5.           Lock-up;
            Transfer Restrictions.

       

      (a)          The Sponsor and the Insiders agree
          that they shall not Transfer any Founder Shares (the “Founder Shares Lock-up”) until the earliest of (A) one year after the completion of
          the Company’s initial Business Combination and (B) the date following the completion of an initial Business Combination on which the Company completes a liquidation, merger, share exchange, reorganization or other similar transaction that results
          in all of the Public Shareholders having the right to exchange their Ordinary Shares for cash, securities or other property (the “Founder Shares
            Lock-up Period”). Notwithstanding the foregoing, if, subsequent to a Business Combination, the closing price of the Ordinary Shares equals or exceeds $12.00 per share (as adjusted for share splits, share capitalizations, reorganizations,
          recapitalizations and the like) for any 20 trading days within any 30-trading day period commencing at least 150 days after the Company’s initial Business Combination, the Founder Shares shall be released from the Founder Shares Lock-up.

       

      (b)          Subject to the provisions set forth in
          paragraph 5(c), the Sponsor and Insiders agree that they shall not effectuate any Transfer of Private Placement Shares until 30 days after the completion of an initial
          Business Combination.

       

      (c)          Notwithstanding the provisions set
          forth in paragraphs 5(a) and (b), Transfers of the Founder Shares and Private Placement
          Shares are permitted (a) to the Company’s officers or directors, any affiliates or family member of any of the Company’s officers or directors, any members or partners of the Sponsor or their affiliates, any affiliates of the Sponsor, or any
          employees of such affiliates; (b) in the case of an individual, by gift to a member of one of the individual’s immediate family or to a trust, the beneficiary of which is a member of the individual’s immediate family, an affiliate of such person
          or to a charitable organization; (c) in the case of an individual, by virtue of laws of descent and distribution upon death of the individual; (d) in the case of an individual, pursuant to a qualified domestic relations order; (e) by private
          sales or transfers made in connection with the consummation of a Business Combination at prices no greater than the price at which the Founder Shares or Private Placement Shares, as applicable, were originally purchased; (f) by virtue of the
          Sponsor’s organizational documents upon liquidation or dissolution of the Sponsor; (g) to the Company for no value for cancellation in connection with the consummation of its initial Business Combination, (h) in the event of the Company’s
          liquidation prior to the completion of its initial Business Combination; or (i) in the event of completion of a liquidation, merger, share exchange or other similar transaction which results in all of the Company’s Public Shareholders having the
          right to exchange their Ordinary Shares for cash, securities or other property subsequent to the completion of an initial Business Combination; provided, however, that in the case of clauses (a) through (f) these permitted transferees must enter
          into a written agreement agreeing to be bound by these transfer restrictions.

       

      (d)          During the period commencing on the
          effective date of the Underwriting Agreement and ending 180 days after such date, the Sponsor and each Insider shall not, without the prior written consent of the Representatives, Transfer any Ordinary Shares or any other securities convertible
          into, or exercisable or exchangeable for, Ordinary Shares held by it, her or him, as applicable, subject to certain exceptions enumerated in Section 3(p) of the Underwriting Agreement.

       

      
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      6.           Remedies.
        The Sponsor and each of the Insiders hereby agree and acknowledge that (i) each of the Underwriters and the Company would be irreparably injured in the event of a breach by the Sponsor or such Insider of its, her or his obligations, as applicable
        under paragraphs 3, 4, 5, 7, 10 and 11, (ii) monetary damages may not be an adequate remedy for such breach
        and (iii) the non-breaching party shall be entitled to injunctive relief, in addition to any other remedy that such party may have in law or in equity, in the event of such breach.

       

      7.           Payments
            by the Company. Except as disclosed in the Prospectus, neither the Sponsor nor any affiliate of the Sponsor nor any director or officer of the Company nor any affiliate of the directors and officers shall receive from the Company any
        finder’s fee, reimbursement, consulting fee, monies in respect of any payment of a loan or other compensation prior to, or in connection with any services rendered in order to effectuate the consummation of the Company’s initial Business
        Combination (regardless of the type of transaction that it is).

       

      8.           Director
            and Officer Liability Insurance. The Company will maintain an insurance policy or policies providing directors’ and officers’ liability insurance, and the Insiders shall be covered by such policy or policies, in accordance with its
        or their terms, to the maximum extent of the coverage available for any of the Company’s directors or officers.

       

      9.           Termination.
        This Letter Agreement shall terminate on the earlier of (i) the expiration of the Founder Shares Lock-up Period and (ii) the liquidation of the Company; provided, however, that this Letter Agreement shall terminate in the event that the Public
        Offering is not consummated and closed by December 31, 2020; provided further that paragraph 10 of this Letter Agreement shall survive such liquidation.

       

      10.         Indemnification.
          In the event of the liquidation of the Trust Account upon the failure of the Company to consummate its initial Business Combination within the time period set forth in the Charter, the Sponsor (the “Indemnitor”) agrees to indemnify and hold harmless the Company against any and all loss, liability,
          claim, damage and expense whatsoever (including, but not limited to, any and all legal or other expenses reasonably incurred in investigating, preparing or defending against any litigation, whether pending or threatened) to which the Company may
          become subject as a result of any claim by (i) any third party for services rendered or products sold to the Company (except for the Company’s independent auditors) or (ii) any prospective target business with which the Company has discussed
          entering into a transaction agreement (a “Target”); provided,
          however, that such indemnification of the Company by the Indemnitor (x) shall apply only to the extent necessary to ensure that such claims by a third party for services rendered or products sold to the Company or a Target do
          not reduce the amount of funds in the Trust Account to below the lesser of (i) $10.00 per Public Share and (ii) the actual amount per Public Share held in the Trust Account as of the date of the liquidation of the Trust Account if less than
          $10.00 per Public Share due to reductions in the value of the trust assets, in each case net of interest that may be withdrawn to pay the Company’s tax obligations, (y) shall not apply to any claims by a third party or Target who executed a
          waiver of any and all rights to the monies held in the Trust Account (whether or not such waiver is enforceable) and (z) shall not apply to any claims under the Company’s indemnity of the Underwriters against certain liabilities, including
          liabilities under the Securities Act of 1933, as amended. The Indemnitor shall have the right to defend against any such claim with counsel of its choice reasonably satisfactory to the Company if, within 15 days following written receipt of
          notice of the claim to the Indemnitor, the Indemnitor notifies the Company in writing that it shall undertake such defense.

       

      
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      11.         Forfeiture
            of Founder Shares. To the extent that the Underwriters do not exercise their option to purchase additional Ordinary Shares within 45 days from the date of the Prospectus in full (as further described in the Prospectus), the Sponsor
        agrees to automatically surrender to the Company for no consideration, for cancellation at no cost, an aggregate number of Founder Shares so that the number of Founder Shares will equal of 20% of the sum of the total number of Ordinary Shares
        (excluding the Private Placement Shares) and Founder Shares outstanding at such time. The Sponsor and Insiders further agree that to the extent that the size of the Public Offering is increased or decreased, the Company will effect a share
        capitalization or a share repurchase, as applicable, with respect to the Founder Shares immediately prior to the consummation of the Public Offering in such amount as to maintain the number of Founder Shares at 20% of the sum of the total number of
        Ordinary Shares (excluding the Private Placement Shares) and Founder Shares outstanding at such time.

       

      12.         Entire
            Agreement. This Letter Agreement constitutes the entire agreement and understanding of the parties hereto in respect of the subject matter hereof and supersedes all prior understandings, agreements, or representations by or among the
        parties hereto, written or oral, to the extent they relate in any way to the subject matter hereof or the transactions contemplated hereby. This Letter Agreement may not be changed, amended, modified or waived (other than to correct a typographical
        error) as to any particular provision, except by a written instrument executed by (1) each Insider that is the subject of any such change, amendment, modification or waiver and (2) the Sponsor.

       

      13.         Assignment.
        No party hereto may assign either this Letter Agreement or any of its rights, interests, or obligations hereunder without the prior written consent of the other parties. Any purported assignment in violation of this paragraph shall be void and
        ineffectual and shall not operate to transfer or assign any interest or title to the purported assignee. This Letter Agreement shall be binding on the Sponsor, each of the Insiders and each of their respective successors, heirs, personal
        representatives and assigns and permitted transferees.

       

      14.         Counterparts.
        This Letter Agreement may be executed in any number of original or facsimile counterparts, and each of such counterparts shall for all purposes be deemed to be an original, and all such counterparts shall together constitute but one and the same
        instrument.

       

      15.         Effect
            of Headings. The paragraph headings herein are for convenience only and are not part of this Letter Agreement and shall not affect the interpretation thereof.

       

      16.         Severability.
        This Letter Agreement shall be deemed severable, and the invalidity or unenforceability of any term or provision hereof shall not affect the validity or enforceability of this Letter Agreement or of any other term or provision hereof. Furthermore,
        in lieu of any such invalid or unenforceable term or provision, the parties hereto intend that there shall be added as a part of this Letter Agreement a provision as similar in terms to such invalid or unenforceable provision as may be possible and
        be valid and enforceable.

       

      
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      17.         Governing
            Law. This Letter Agreement shall be governed by and construed and enforced in accordance with the laws of the State of New York, without giving effect to conflicts of law principles that would result in the application of the
        substantive laws of another jurisdiction. The parties hereto (i) all agree that any action, proceeding, claim or dispute arising out of, or relating in any way to, this Letter Agreement shall be brought and enforced in the courts of New York City,
        in the State of New York, and irrevocably submit to such jurisdiction and venue, which jurisdiction and venue shall be exclusive, and (ii) waive any objection to such exclusive jurisdiction and venue or that such courts represent an inconvenient
        forum.

       

      18.         Notices.
        Any notice, consent or request to be given in connection with any of the terms or provisions of this Letter Agreement shall be in writing and shall be sent by express mail or similar private courier service, by certified mail (return receipt
        requested), by hand delivery or facsimile or other electronic transmission.

       

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              Sincerely,

            
	 	 
	 	
              ARYA SCIENCES HOLDINGS III

            
	 	 	 
	 	
              By:

            	
              /s/ Adam Stone

            
	 	
              Name:

            	
              Adam Stone

            
	 	
              Title:

            	
              Authorized Signatory

            


      

      

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              /s/ Joseph Edelman

            
	 	
              Joseph Edelman

            


      

      

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              /s/ Adam Stone

            
	 	
              Adam Stone

            


      

      

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              /s/ Michael Altman

            
	 	
              Michael Altman

            


      

      

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              /s/ Konstantin Poukalov

            
	 	
              Konstantin Poukalov

            


      

      

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              /s/ Saqib Islam

            
	 	
              Saqib Islam

            


      

      

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              /s/ Bradley L. Campbell

            
	 	
              Bradley L. Campbell

            


      

      

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              /s/ Todd Wider

            
	 	
              Todd Wider

            


      

      

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              Acknowledged and Agreed:

            	 
	 	 
	
              ARYA SCIENCES ACQUISITION CORP III

            	 
	 	 	 
	
              By:

            	
              /s/ Adam Stone

            	 
	
              Name:

            	
              Adam Stone

            	 
	
              Title:

            	
              Chief Executive Officer

            	 


      

      

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