CONSULTING AGREEMENT

Exhibit 10.45

CONSULTING AGREEMENT

This Consulting Agreement (“Agreement”) is made and entered into by and between Amarin Corporation plc (the “Company”), and Joseph S. Zakrzewski (“Executive”) as of November 10, 2010. The Company desires to retain Executive as an independent contractor to perform consulting services for the Company and Executive is willing to perform such services, on terms set forth more fully below. In consideration of the mutual promises contained herein, the parties agree as follows:

1. Services. Executive will serve as the Company’s Chief Executive Officer and Executive Chairman and will have such duties, responsibilities and authorities as determined by the Company’s Board of Directors (the “Services”). Executive agrees to devote such time to these Services as is necessary to perform them with the understanding that for so long as he serves as Chief Executive Officer his service to the Company will be his primary business commitment and that Executive will work two and one-half (2.5) days per week. Notwithstanding the foregoing, the Executive may manage his personal investments, engage in religious, charitable or other community activities, and, subject to the terms of this Section, provide professional services to third parties and serve on corporate and industry boards, as long as such activities do not pose an actual direct conflict of interest and do not materially interfere with the Executive’s performance of his duties to the Company as set forth herein. Executive represents that set forth on Appendix A is a comprehensive list of all outside professional activities with which he is currently involved. From time to time, the Company may ask Executive to work with and at the direction of the Company’s legal counsel in order to provide assistance on certain legal matters. It is the Company’s intention that such work be covered by the attorney-client privilege to the maximum extent permitted by law. In addition to the Executive’s role as Chief Executive Officer and Executive Chairman of the Company, the Executive acknowledges and agrees that he may be required, without additional compensation, to perform services for certain affiliated entities of the Company, including without limitation Amarin Pharma, Inc., and to accept any reasonable office or position with any such affiliate as the Company’s Board of Directors (the “Board”) may require, including, but not limited to, service as an officer or director of any such affiliate. For the avoidance of doubt, Executive may perform the Services from a remote location, and shall not be required to commute to the Company’s Mystic, Connecticut facility or any other facility of the Company.

2. Consulting Fees; Stock Options; Discretionary Bonus; Expenses. The Company shall pay the Executive $62,500 per calendar quarter as sole compensation for the performance of the Services, which amount is inclusive of the $37,500 per calendar quarter previously paid to the Executive for his service to the Company pursuant to that certain letter agreement between the Company and the Executive dated October 12, 2009 (the “Letter Agreement”). In the event that Executive ceases to serve as the Company’s Chief Executive Officer, for any reason, but continues to serve as the Executive Chairman or Chairman of the Board, then, for so long as Executive continues to serve in such capacity, the Company shall pay the Executive $37,500 per calendar quarter as sole compensation for the performance of such services to the Company. The

amount paid to the Executive pursuant to the first or second sentence of this Section 2 shall be referred to herein as the “Consulting Fees”. The Consulting Fees will be paid to Executive on a quarterly basis and reported by the Company to taxing authorities on Form 1099. In consideration of Executive’s service to the Company as Chief Executive Officer, Executive will be granted options to purchase 1,750,000 Ordinary Shares, par value £0.50 per share (and represented by American Depository Shares, or ADSs) (the “CEO Options”), which represents approximately 1.5% of the Company’s outstanding equity capitalization based on approximately 102,194,949 Ordinary Shares and options to purchase approximately 11,658,601 Ordinary Shares currently outstanding (excluding warrants). For the avoidance of doubt, the CEO Options are in addition to the options granted to Executive pursuant to the Letter Agreement (the “Board Member Options”). The exercise price per share of the CEO Option shares will be the closing price of the Company’s ADSs on the NASDAQ Capital Market on Thursday, November 11, 2010. Twenty five percent (25%) of the CEO Option shares shall be fully vested and immediately exercisable on the date of grant, with the remainder to vest in three equal annual installments, beginning on the first anniversary of the Effective Date, so long as Executive continues to serve as the Company’s Chief Executive Officer. In the event that the Executive ceases to serve as the Company’s Chief Executive Officer, for any reason, other than as set forth in the immediately following sentence, the CEO Option shares shall cease vesting and the CEO Option award, to the extent then vested and exercisable, shall be exercisable for twelve (12) months following such event, as provided in Section 6(a)(xi)(C) (Other Termination) under the Company’s 2002 Stock Option Plan, notwithstanding the fact that the Executive may continue to serve as Executive Chairman, Chairman or in some other capacity with the Company. As provided in the Company’s 2002 Stock Option Plan, if within two years following a Change of Control (as defined in the 2002 Stock Option Plan), the Executive is removed as the Company’s Chief Executive Officer for any reason other than for Cause (as defined in the 2002 Stock Option Plan), all of the Executive’s CEO Option unvested shares will vest in full. For the avoidance of doubt, (i) the Board Member Options shall continue to vest subject to, and in accordance with, the terms of that certain Award Agreement dated December 21, 2009 and the terms of the 2002 Stock Option Plan, notwithstanding the fact that the Executive may cease to serve as the Company’s Chief Executive Officer, and (ii) provided that the Executive is then servicing as a director, in the event of a Change of Control, the vesting of the Board Member Options shall be governed by Section 6(a)(viii)(1) of the 2002 Stock Option Plan. Except as modified by the terms of this Agreement, the terms and conditions set forth in the 2002 Stock Option Plan and applicable stock option agreement shall govern the CEO Option award. In addition, for so long as the Executive continues to serves as the Company’s Chief Executive Officer, the Executive will be eligible to receive an annual performance bonus as determined by the Board (or the Remuneration Committee thereof) (the “Annual Bonus”). The Company will target the Annual Bonus at 50% of the Executive’s annual Consulting Fees, which shall be prorated for 2010. Any such bonuses shall be payable in the absolute discretion of the Board (or the Remuneration Committee thereof), taking into account the performance of the Company and Executive’s personal performance. The Company shall also reimburse Executive for all reasonable travel and out-of-pocket expenses incurred by Executive in performing Services pursuant to this Agreement consistent with the Company’s expense reimbursement policies.

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3. Nondisclosure of Confidential Information. “Confidential Information” means all trade secrets and confidential or proprietary information, whether or not in writing, concerning the Company’s business, technology, business relationships or financial affairs which the Company has not released to the general public. Executive will not, at any time, without the Company’s prior written permission, either during or after the term of this Agreement, disclose any Confidential Information to anyone outside of the Company, or use or permit to be used any Confidential Information for any purpose other than the performance of the Services for or on behalf of the Company. In addition, Executive understands that the Company is now and may hereafter be subject to non-disclosure or confidentiality agreements with third persons which require the Company to protect or refrain from use of its or their confidential information. Executive agrees to be bound by the terms of such agreements in the event Executive has access to such confidential information.

4. Ownership. Executive will make full and prompt disclosure to the Company of all inventions, discoveries, designs, developments, methods, modifications, improvements, ideas, products, processes, techniques, know-how, trade secrets, graphics or images, and audio or visual works and other works of authorship (collectively “Developments”), whether or not patentable or copyrightable, that are created, made, conceived or reduced to practice by Executive (alone or jointly with others) in performance of the Services during the term of this Agreement. Executive acknowledges that all work performed by Executive within the scope of the Services is on a “work for hire” basis, and Executive hereby assigns and transfers and, to the extent any such assignment cannot be made at present, will assign and transfer, to the Company and its successors and assigns all Executive’s right, title and interest in all Developments that (i) relate to the business of the Company or any customer of the Company or any of the products or services being researched, developed, manufactured, performed or sold by the Company or which may be used with such products or services; or (ii) result from tasks assigned to Executive by the Company and/or the Services; or (iii) result from the use of premises or personal property (whether tangible or intangible) owned, leased or contracted for by the Company (“Company-Related Developments”). For the avoidance of doubt, this Agreement does not obligate Executive to assign to the Company any Development which is developed on Executive’s own time and does not relate to the business efforts or research and development efforts in which, during the term of this Agreement, the Company actually is engaged or reasonably would be engaged, and does not result from the use of premises or equipment owned or leased by the Company.

5. Documents; Property. All Developments, files, letters, notes, memoranda, reports, records, data, layouts, charts, quotations and proposals, specification sheets, or other written, photographic or other tangible material containing Confidential Information, whether created by Executive or others, which come into Executive’s custody or possession (“Documents”), are the exclusive property of the Company to be used by Executive only in the performance of the Services. Further, any property situated on the Company’s premises or owned or leased by the Company, including without limitation computers, electronic files, disks and other storage media, filing cabinets or other work areas, is subject to inspection by the Company at any time with or without notice. In the event that the Executive ceases to serve as Chief Executive Officer and a Board member, Executive will promptly deliver to the Company all Documents, Company property and other materials of any nature pertaining to the Confidential Information of the Company and to the Services, and will not take or keep in Executive’s possession any of the foregoing or any copies.

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6. Noncompetition and Nonsolicitation. During the Executive’s services to the Company as Chief Executive Officer, Executive (i) will not, directly or indirectly, whether as owner, partner, shareholder, consultant, agent, employee, co-venturer or otherwise, engage, participate, assist or invest in any business activity anywhere in the United States or Europe that develops, manufactures or markets any products that are competitive with the products of the Company, or products that the Company or its subsidiaries or corporate affiliates (the “Company” for purposes of this Section 6), has under development or that are the subject of active planning at any time during Executive’s service to the Company as Chief Executive Officer (a “Competing Business”); and (ii) will refrain from directly or indirectly employing, attempting to employ, contracting with, recruiting or otherwise soliciting, inducing or influencing any employee to leave employment with the Company or any subsidiary of Company other than general solicitations of employment not directly targeting employees of the Company, (such as through general advertisements, search firms, etc.), and (iii) will refrain from soliciting or encouraging any independent contractor to terminate or otherwise modify adversely its business relationship with the Company or any of it subsidiaries. The Executive understands that the restrictions set forth in this Section 6 are intended to protect the Company’s interest in its Confidential Information (defined above) and established employee, customer and supplier relationships and goodwill, and agrees that such restrictions are reasonable and appropriate for this purpose. Notwithstanding the foregoing, the Executive may own up to one percent (1%) of the outstanding stock of a publicly held corporation, which constitutes or is affiliated with a Competing Business. For the avoidance of doubt, Executive’s assistance with any disputes and litigation associated with his role with Reliant Pharmaceuticals, including, without limitation, litigation related to Omacor/Lovaza, shall not be construed as a breach of this Section 6.

7. Avoidance of Conflict of Interest. Executive represents and warrants that Executive has no outstanding agreement or obligation that is in conflict with any of the provisions of this Agreement, or that would preclude Executive from fully complying with the provisions hereof, and further certifies that Executive will not enter into such conflicting agreement during the term of this Agreement. Executive will advise the Company at such time as any activity of either the Company or another business presents Executive with an actual direct conflict of interest. Executive will take whatever action is requested by the Company to resolve any such conflict. Executive further represents and warrants that it has full power and authority to enter into this Agreement and perform its obligations hereunder. The Company acknowledges that Executive is currently a venture partner with OrbiMed Advisors LLC, which, together with its affiliates (collectively “OrbiMed”), is a shareholder of the Company. Without limiting the generality of the foregoing, for so long as the Executive renders services to the Company, the Executive hereby agrees that he shall not engage in any employment, consulting or other business activity (whether full-time or part-time) with OrbiMed that would create a conflict of interest with the Company. This Section 7 shall only apply while Executive is Chief Executive Officer.

8. Indemnification. If Executive is made a party, or is threatened to be made a party, to any action, suit or proceeding, whether civil, criminal, administrative or investigative, by reason of the performance of the Services or the fact that Executive is an officer or director of the Company or provided services to an affiliate thereof, Executive shall be indemnified and held harmless by the Company and such affiliate to the fullest extent permitted or authorized by applicable law and its organizational documents, against all cost, expense, liability and loss

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reasonably incurred or suffered by Executive in connection therewith. Executive shall be covered under the Company’s directors’ and officers’ liability insurance policy. This Section 8 shall be in addition to, and not in lieu of, Company’s indemnification obligations set forth in that certain Deed of Indemnity between Company and Executive dated February 16, 2010 (“Deed of Indemnity”) and that certain Indemnification Agreement between Amarin Pharma Inc. and Executive dated September 15, 2009 (the “Indemnification Agreement”).

9. Term. This Agreement will commence on November 10, 2010, and will continue until terminated as provided below in Section 10.

10. Termination; Continuation of Payments. The Company or the Executive may terminate this Agreement at any time and for any reason upon giving thirty (30) days prior written notice thereof to the other party. Any such notice shall be addressed to Executive or the Company, respectfully, at the address shown below or such other address as Executive may notify the Company of and shall be deemed given if delivered as set forth pursuant to Section 17 below. The Company may, in addition to any other rights it may have at law or in equity, terminate this Agreement immediately and without prior notice if Executive refuses to or is unable to perform the Services or is in breach of any material provision of this Agreement. Upon such termination all rights and duties of the parties with respect to the Executive providing Services and the Company compensating the Executive for such Services shall cease except the Company shall be obliged to pay, within thirty (30) days of the effective date of termination, all Consulting Fees for services actually performed and reimbursable expenses actually incurred prior to termination, if any, in accordance with the provisions of Section 2. For the avoidance of doubt, the Deed of Indemnity and Indemnification Agreement shall survive the expiration or earlier termination of this Agreement. Notwithstanding the foregoing, if at any time prior to Executive’s voluntary resignation as Chief Executive Officer or Executive’s voluntary termination of this Agreement, in the event that the Company shall remove the Executive as Chief Executive Officer or terminate this Agreement without Cause (as defined below), the Executive shall (i) be entitled to continue to receive Consulting Fees for the twelve (12) month period following the effective date of such removal and/or termination, and (ii) be eligible to receive his pro rata Annual Bonus, as determined by the Board (or the Remuneration Committee thereof) and consistent with Executive’s contribution to such objectives as part of the Annual Bonus, for the year in which the Executive is terminated (based on the number of days the Executive served as Chief Executive Officer during such calendar year), such bonus to be paid at the same time as annual bonuses are paid to the Company’s other senior executives. The Executive’s right to receive such payments shall be conditioned upon the Executive’s execution and delivery of a customary release and non-disparagement agreement in favor of the Company. Notwithstanding the foregoing, in the event that the Executive voluntarily resigns as Chief Executive Officer or otherwise voluntarily terminates this Agreement or in the event that this Agreement is terminated due to the Executive’s death or disability, the Executive shall not be entitled to the continuation of Consulting Fees or his pro rata Annual Bonus as provided above; provided however, that (x) the Executive shall be eligible to receive a pro rata Annual Bonus to the extent provided in the immediately following sentence, and (y) for so long as the Executive continues to serve as Chairman of the Board, he shall be entitled to receive those consulting fees described in the second sentence of Section 2 of this Agreement. In the event that the Company elects to hire a new Chief Executive Officer (including, without limitation, upon your recommendation), you agree to resign as Chief Executive Officer, which resignation shall be

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deemed a voluntary resignation for purposes of this Agreement; provided however, that in such event, you shall be eligible to receive to a pro rata Annual Bonus to the extent provided above. For purposes of this Agreement, “Cause” shall mean: (i) conduct by the Executive constituting an act of material misconduct in connection with the performance of the Executive’s duties, including, without limitation, misappropriation of funds or property of the Company other than the occasional, customary and de minimis use of Company property for personal purposes; (ii) the commission by the Executive of (A) any felony; or (B) a misdemeanor involving moral turpitude, deceit, dishonesty or fraud; (iii) any conduct by the Executive that would reasonably be expected to result in material injury or reputational harm to the Company or any of its subsidiaries and affiliates if the Executive were retained in the Executive’s position; (iv) continued non-performance or unsatisfactory performance by the Executive of the Employee’s responsibilities as reasonably determined by the Company’s Board of Directors; (v) a breach by the Executive of any of the provisions contained this Agreement including, without limitation, any of the provisions of Sections 3 and 6 hereof; (vi) a material violation by the Executive of any of the Company’s written policies or procedures provided that, other than in the case of clause (B) above or other noncurable events, Executive is provided with written notice and fifteen (15) days to cure.

11. Survival. Notwithstanding anything herein to the contrary, the provisions of this Agreement shall survive termination or expiration of this Agreement to the extent to necessary to accomplish the purpose(s) of the provision.

12. Independent Contractor; Taxes. It is understood and agreed that Executive will be an independent contractor. Executive will perform Services under the Company’s Board of Directors’ general direction as to the result of activity but Executive shall determine, in Executive’s discretion, the manner and means by which the Services are accomplished, subject to the express condition that Executive will at all times comply with applicable law. Executive expressly waives any right to participate in any of the Company’s employee benefit plans or perquisites. Executive further disclaims any intention or right to participate in any of the Company’s employee benefit plans or perquisites even if Executive’s status with the Company is determined by a third party tribunal to be that of an employee. Executive acknowledges and agrees that Executive is obligated to report as income all Consulting Fees received by Executive pursuant to this Agreement, and Executive agrees to and acknowledges the obligation to pay all taxes, including without imitation all federal and state income tax, social security taxes and unemployment, disability insurance and workers’ compensation applicable to Executive and any person who performs Services in connection with this Agreement.

If, at any time, Executive’s status with the Company as an independent contractor changes or Executive is ever deemed to be an employee of the Company, each of the covenants set forth above and this Agreement remain in full force and effect in its entirety until and unless it is replaced with a subsequent and superseding agreement.

13. Amendment. This Agreement may not be amended in any respect other than by written instrument executed by the party against whom enforcement is sought.

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14. Entire Agreement. The terms and conditions herein contained and in the Indemnification Agreement constitute the entire agreement between the parties and supersede all previous agreements and understandings, whether oral or written, between the parties hereto with respect to the subject matter hereof, and no agreement or understanding varying or extending the same shall be binding upon either party hereto unless in a written document which expressly refers to this Agreement and which is signed by the party to be bound thereby. Without limiting the forgoing, the Company and the Executive hereby acknowledge and agree that the Letter Agreement is terminated and superseded by this Agreement in all respects.

15. Governing Law and Personal Jurisdiction. This Agreement shall be governed by and construed in accordance with the internal laws of the State of Connecticut, without reference to its principles of conflict of laws.

16. Changes. Executive understands that, absent an express amendment, Executive’s obligations under this Agreement will continue in accordance with its express terms regardless of any changes in nature of Executive’s Services, compensation or other terms and conditions of the Executive relationship.

17. Notices. Any notice hereby required or permitted to be given shall be sufficiently given if in writing and delivered in person, by facsimile transmission, electronic mail, overnight delivery service or U.S. mail, to either party at the last known address of such party or such other address as shall have been designated by written notice by such party to the other party. If by mail, delivery shall be deemed effective three (3) business days after mailing in accordance with the above provisions.

18. No Waiver. No waiver of any term or condition of this Agreement shall be valid or binding on either party unless the same shall be been mutually assented to in writing by both parties. The failure of either party to enforce at any time any of the provisions of this Agreement, or the failure to require at any time performance by the other party of any of the provisions of this Agreement, shall in no way be construed to be a present or future waiver of such provisions, nor in any way affect the right of either party to enforce each and every such provision thereafter. The express waiver by either party of any provision, condition or requirement of this Agreement shall not constitute a waiver of any future obligation to comply with such provision, condition or requirement.

19. Counterparts. This Agreement may be signed in one or more counterparts.

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IN WITNESS WHEREOF, the parties hereto have caused to be executed or executed this Consulting Agreement as of the day and year first above written.

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Appendix A

Outside Professional Activities

Venture Partner, OrbiMed Advisors LLC

Chairman of the Board, Zelos Therapeutics, Inc.

Chairman of the Board, Promedior Inc.

Chairman of the Board, Xcellerex, Inc.

Board Member, Insulet Corporation

Board Member, Rapid Bio Microsystems, Inc.