Exhibit 4.11


 


WARRANT AGENT AGREEMENT


 


This Warrant Agent Agreement (this “Agreement”)
is made effective as of April 8, 2021, by and between Zion Oil & Gas, Inc., a Delaware corporation having its principal place of business
at 12655 North Central Expressway, Suite 1000, Dallas, Texas 75243 (the “Company”), and American Stock Transfer
& Trust Company, LLC, a New York limited liability trust company with offices at 6201 15th Avenue, Brooklyn, NY 11219 (“AST”)
and is an amendment to the Warrant Agent Agreement dated August 1, 2014 between the Company and AST, to the February 2, 2015 amendment
to the Warrant Agent Agreement, to the November 1, 2016 amendment to the Warrant Agent Agreement, to the May 22, 2017 amendment to the
Warrant Agent Agreement, to the October 12, 2017 amendment, to the February 1, 2018 amendment to the Warrant Agent Agreement, to the April
2, 2018 amendment to the Warrant Agreement, to the August 21, 2018 amendment to the Warrant Agreement, to the December 7, 2018 amendment
to the Warrant Agent Agreement, to the January 15, 2021 amendment to the Warrant Agent Agreement and to the February 1, 2021 amendment
to the Warrant Agent Agreement by the expansion of the Unit option program. 


 


WHEREAS, the Company has implemented a
Dividend Reinvestment and Common Stock Purchase Plan (hereinafter “DSPP”) and AST is administering the DSPP
as the Plan agent (the “Plan Agent”) and Warrant agent (the “Warrant Agent”), effective
August 1, 2014, (1) under a Warrant Agreement dated August 1, 2014 that is still in effect for the $2.50 Unit option program and as the
continuation of AST as the Warrant Agent under the DSPP for the Warrant ZNWAA, (2) under a Warrant Agent Agreement dated February 2, 2015
that is still in effect for the $4.00 Unit option program for the Warrant ZNWAD, (3) under a Warrant Agent Agreement dated November 1,
2016 that is still in effect for the $10.00 Unit option program for the Warrant ZNWAE, (4) under a Warrant Agent Agreement dated May 22,
2017 for the Warrant ZNWAF that is still in effect for the $250.00 Unit option program, (5) under a Warrant Agent Agreement dated October
12, 2017 for the Warrant ZNWAG that is still in effect for the $250.00 Unit option program, (6) under a Warrant Agent Agreement dated
February 1, 2018 for the Warrant ZNWAH, (7) under a Warrant Agent Agreement dated April 2, 2018 for the Warrant ZNWAI, (8) under a Warrant
Agent Agreement dated August 21, 2018 for the Warrant ZNWAJ, (9) under a Warrant Agent Agreement dated December 7, 2018 for the Warrant
ZNWAK, (10) under a Warrant Agent Agreement dated April 23, 2019 for the Warrant ZNWAL, (11) under a Warrant Agent Agreement dated January
15, 2021 for the Warrant ZNWAM, (12) under Warrant Agent Agreement dated February 1, 2021 for the Warrant ZNWAN and (13) as the continuation
of AST as the Warrant Agent under the DSPP for the Warrant ZNWAO dated April 8, 2021;


 


WHEREAS,
pursuant to the DSPP, the Company is offering a new unit option program consisting of a new Unit (each a “Unit”
and collectively the “Units”) of its securities to existing stockholders and investors, with each Unit (priced
at $250.00 each) is comprised of (i) a certain number of shares of Common Stock determined by dividing
$250.00 (the price of one Unit) by the average of the high and low sale prices of the Company’s publicly traded common stock as
reported on the OTCQX on the Unit Purchase Date and (ii) Common Stock purchase warrants to purchase an additional fifty (50) shares of
Common Stock at a per share exercise price of $0.25. The Unit Option begins on April 12, 2021 and is scheduled to terminate on May 12,
2021. The participant’s Plan account will be credited with the number of shares of the Company’s
Common Stock and warrants that are acquired under the Units purchased. Each warrant affords the investor the opportunity to purchase one
share of our Common Stock at an exercise price of $0.25 per share (each “Warrant” and collectively the “Warrants”)
and each Unit may be purchased at a per Unit price of $250.00;


 




     



     


    

 


WHEREAS, for Plan participants who enroll
into the Unit Program with the purchase of at least one Unit and also enroll in the separate Automatic Monthly Investments (“AMI”)
program at a minimum of $50.00 per month or more, will receive an additional ten (10) Warrants at an exercise price of $0.25 during this
Unit Option Program. The ten (10) additional warrants are for enrolling into the AMI program. Existing subscribers to the AMI are entitled
to the additional ten (10) warrants once, if they purchase at least one (1) Unit during the Unit program.


 


WHEREAS, the new Warrants will be exercisable
on June 11, 2021, which is the first trading day after the 30th day following the Unit Option Termination Date (i.e., on May
12, 2021) and continue to be exercisable for two (2) years after the exercise date at a per share exercise price of $0.25 for the Warrant
as notated by the Company as ZNWAO until June 12, 2023;


 


WHEREAS, the Company is utilizing the
Registration Statement on Form S-1 (Registration No. 333-235299), as amended, which was declared effective by the SEC on December 11,
2019 (the “Registration Statement”) and Amendment No. 3 filed April 8, 2021 to facilitate the trading of the
shares of Common Stock included in the new Units and the shares of Common Stock underlying the Warrants that are included in the Units
as well as the Warrants;


 


WHEREAS, the shares of Common Stock included
in the Units are tradable on the OTCQX under the symbol ZNOG and, following the closing of the Unit program, the shares of Common Stock
underlying the Warrants, will be tradable after Warrant exercise on the OTCQX under the symbol ZNOG;


 


WHEREAS, the Company desires AST to act
on behalf of the Company, and AST is willing to so act, in connection with the issuance, registration, transfer, exchange, redemption
and exercise of the Warrants (in such capacity, the “Warrant Agent”) herein described;


 


WHEREAS, the Company desires to provide
for the form and provisions of the Warrant, the terms upon which it shall be issued and exercised, and the respective rights, limitation
of rights, and immunities of the Company, the Warrant Agent, and the holders of the Warrants; and


 


WHEREAS, all acts and things have been
done and performed which are necessary to make the Warrants, when executed on behalf of the Company and countersigned by or on behalf
of the Warrant Agent, as provided herein, the valid, binding and legal obligations of the Company, and to authorize the execution and
delivery of this Agreement.


 


NOW, THEREFORE, in consideration of the
mutual agreements herein contained, the parties hereto agree as follows:


 


1.   Appointment of Warrant Agent. The Company
hereby appoints the Warrant Agent to act as agent for the Company for the Warrants herein described, and the Warrant Agent hereby accepts
such appointment and agrees to perform the same in accordance with the terms and conditions set forth in this Agreement.


   


2.   New Warrant.


 


2.1   Form of Warrant. The Warrant shall be issued
in registered form or held in book entry form by AST as Warrant Agent. The Warrant shall be in substantially the form of Exhibit
A hereto, the provisions of which are incorporated herein, and shall be signed by, or bear the facsimile signature of, the Executive
Chairman and Secretary/Treasurer of the Company and shall bear a facsimile of the Company’s seal. In the event the person whose
facsimile signature has been placed upon any Warrant shall have ceased to serve in the capacity in which such person signed the Warrant
before such Warrant is issued, it may be issued with the same effect as if he or she had not ceased to be such at the date of issuance.


 




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2.2   Effect of Countersignature. Unless and until
countersigned by the Warrant Agent pursuant to this Agreement, a Warrant shall be invalid and of no effect and may not be exercised by
the holder thereof, unless acknowledged and held in book entry form by the Warrant Agent.


 


2.3   Registration.


 


2.3.1   Warrant Register. The Warrant Agent shall
maintain books (“Warrant Register” or also referred to as “book entry form”) for the
registration of original issuance and the registration of transfer of the Warrants, if the Warrants are not held in book entry form by
Warrant Agent. Upon the initial issuance of the Warrants unless held in book entry form by the Warrant Agent, the Warrant Agent shall
issue and register the Warrants in the names of the respective holders thereof in such denominations and otherwise in accordance with
instructions delivered to the Warrant Agent by the Company.


 


2.3.2   Registered Holder. Prior to due presentment
for registration of transfer of any Warrant, the Company and the Warrant Agent may deem and treat the person in whose name such Warrant
shall be registered upon the Warrant Register (“registered holder”), as the absolute owner of such Warrant and
of each Warrant represented thereby (notwithstanding any notation of ownership or other writing on the Warrant Certificate made by anyone
other than the Company or the Warrant Agent), for the purpose of any exercise thereof, and for all other purposes, and neither the Company
nor the Warrant Agent shall be affected by any notice to the contrary.


 


3.   Terms and Exercise of Warrants.


 


3.1   Warrant Price. Each Warrant shall, when
countersigned by the Warrant Agent, entitle the registered holder thereof, subject to the provisions of such Warrant and this Warrant
Agreement, to purchase from the Company the number of shares of Common Stock stated therein, at the price of $0.25 per share, subject
to the adjustments provided in this Section 3.1 and Section 4 hereof. The term “Warrant Price” as used in this Warrant Agreement
refers to the price per share at which Common Stock may be purchased at the time a Warrant is exercised. The Company in its sole discretion
may lower the Warrant Price at any time prior to the Expiration Date for a period of not less than ten business days, provided that any
such reduction shall be identical among all of the Warrants.


 


3.2   Duration of Warrants. A Warrant may be exercised
only during the period commencing on June 11, 2021, which is the first trading day after the 30th day following the Unit Option
Termination Date (i.e., on May 12, 2021) and continue to be exercisable for two (2) year after the exercise date, terminating at 5:00
p.m., Eastern Standard Time. Notwithstanding the foregoing, no Warrant shall be exercisable unless, at the time of exercise, a registration
statement relating to the Common Stock issuable upon the exercise of such Warrant is effective and current and a prospectus is available
for use by the holders thereof and the Common Stock has been qualified or deemed to be exempt under the securities laws of the state of
residence of the holder of such Warrants. The period during which a Warrant may be exercised shall be deemed the “Exercise
Period” and the termination of such Exercise Period shall be deemed the “Expiration Date.” Each
Warrant not exercised on or before the Expiration Date shall become void, and all rights thereunder and all rights in respect thereof
under this Agreement shall cease at the close of business on the Expiration Date. The Company in its sole discretion may extend the duration
of the Warrants by delaying the Expiration Date; provided, however, the Company will provide notice to registered holders of the Warrants
of such extension of not less than 20 days and, further provided that any such extension shall be identical in duration among all of the
Warrants.


 




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3.3   Exercise of Warrants.


 


3.3.1   Payment. Subject to the provisions of
the Warrants and this Agreement, a Warrant, when countersigned by the Warrant Agent, may be exercised by the registered holder thereof
by surrendering it at the office of the Warrant Agent, or at the office of its successor as Warrant Agent, in Brooklyn, New York, with
the subscription form, as set forth in the Warrant, or exercised by other electronic means acceptable to the Company, duly executed by
paying in full, by bank check, bank wire, other electronic bank payment method, or other legal currency means of payment acceptable by
the Company and payable to the order of the Company, the Warrant Price for each full share of Common Stock as to which the Warrant is
exercised and any and all applicable taxes due in connection with the exercise of the Warrant, the exchange of the Warrant for the Common
Stock and the issuance of the Common Stock.


 


3.3.2   Issuance of Certificates. As soon as practicable
after the exercise of any Warrant and the clearance of the funds in payment of the Warrant Price, the Company shall issue to the registered
holder of such Warrant a certificate or certificates for the number of full shares of Common Stock to which he, she or it is entitled,
registered in such name or names as may be directed by him, her or it, and if such Warrant shall not have been exercised in full, a new
countersigned Warrant for the number of shares as to which such Warrant shall not have been exercised, unless the Common Stock is to be
held in book entry form by AST without the issuance of a certificate and any remaining balance of Warrants to be maintained in book entry
form by the Warrant Agent. Notwithstanding the foregoing, the Company shall not be obligated to deliver or to recognized in book entry
form any securities pursuant to the exercise of a Warrant unless (i) a registration statement under the Act with respect to the Common
Stock issuable upon such exercise is effective, or (ii) in the opinion of counsel to the Company, the exercise of the Warrants is exempt
from the registration requirements of the Act and such securities are qualified for sale or exempt from qualification under applicable
securities laws of the states or other jurisdictions in which the registered holders reside. Warrants may not be exercised by, or securities
issued to, any registered holder in any state in which such exercise or issuance would be unlawful. In no event will the Company be required
to provide the registered holder of a warrant with a net-cash settlement or other consideration in lieu of physical settlement in shares
of Common Stock, regardless of whether the Common Stock underlying the Warrants is registered pursuant to an effective registration
statement.


 


3.3.3   Valid Issuance. All shares of Common Stock
issued upon the proper exercise of a Warrant in conformity with this Agreement shall be validly issued, fully paid and nonassessable.


 


3.3.4   Date of Issuance. Each person in whose
name any such certificate for shares of Common Stock is issued shall for all purposes be deemed to have become the holder of record of
such shares on the date on which the Warrant was surrendered and payment of the Warrant Price was made, irrespective of the date of delivery
of such certificate or the recording by book entry, except that, if the date of such surrender and payment is a date when the stock transfer
books of the Company are closed, such person shall be deemed to have become the holder of such shares at the close of business on the
next succeeding date on which the stock transfer books are open.


 




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4.   Adjustments.


 


4.1   Stock Dividends Split Ups. If after the
date hereof, and subject to the provisions of Section 4.6 below, the number of outstanding shares of Common Stock is increased by a stock
dividend payable in shares of Common Stock, or by a split up of shares of Common Stock, or other similar event, then, on the effective
date of such stock dividend, split up or similar event, the number of shares of Common Stock issuable on exercise of each Warrant shall
be increased in proportion to such increase in outstanding shares of Common Stock. For purposes of clarification, no adjustment shall
be made in the event of a rights offering, or a distribution of rights treated as a dividend to all shareholders of record, or similar
transactions.


 


4.2   Aggregation of Shares. If after the date
hereof, and subject to the provisions of Section 4.6, the number of outstanding shares of Common Stock is decreased by a consolidation,
combination, reverse stock split or reclassification of shares of Common Stock or other similar event, then, on the effective date of
such consolidation, combination, reverse stock split, reclassification or similar event, the number of shares of Common Stock issuable
on exercise of each Warrant shall be decreased in proportion to such decrease in outstanding shares of Common Stock.


   


4.3   Adjustments in Exercise Price. Whenever
the number of shares of Common Stock purchasable upon the exercise of the Warrants is adjusted, as provided in Section 4.1 and 4.2 above,
the Warrant Price shall be adjusted (to the nearest cent) by multiplying such Warrant Price immediately prior to such adjustment by a
fraction (x) the numerator of which shall be the number of shares of Common Stock purchasable upon the exercise of the Warrants immediately
prior to such adjustment, and (y) the denominator of which shall be the number of shares of Common Stock so purchasable immediately thereafter.


 


 4.4   Replacement of Securities upon Reorganization,
etc. In case of any reclassification or reorganization of the outstanding shares of Common Stock (other than a change covered by Section
4.1 or 4.2 hereof or that solely affects the par value of such shares of Common Stock), or in the case of any merger or consolidation
of the Company with or into another corporation (other than a consolidation or merger in which the Company is the continuing corporation
and that does not result in any reclassification or reorganization of the outstanding shares of Common Stock), or in the case of any sale
or conveyance to another corporation or entity of the assets or other property of the Company as an entirety or substantially as an entirety
in connection with which the Company is dissolved, the Warrant holders shall thereafter have the right to purchase and receive, upon the
basis and upon the terms and conditions specified in the Warrants and in lieu of the shares of Common Stock of the Company immediately
theretofore purchasable and receivable upon the exercise of the rights represented thereby, the kind and amount of shares of stock or
other securities or property (including cash) receivable upon such reclassification, reorganization, merger or consolidation, or upon
a dissolution following any such sale or transfer, that the Warrant holder would have received if such Warrant holder had exercised his,
her or its Warrant(s) immediately prior to such event; and if any reclassification also results in a change in shares of Common Stock
covered by Section 4.1 or 4.2, then such adjustment shall be made pursuant to Sections 4.1, 4.2, 4.3 and this Section 4.4. The provisions
of this Section 4.4 shall similarly apply to successive reclassifications, reorganizations, mergers or consolidations, sales or other
transfers.


 




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4.5   Notices of Changes in Warrant. Upon every
adjustment of the Warrant Price or the number of shares issuable on exercise of a Warrant, the Company shall give written notice thereof
to the Warrant Agent, which notice shall state the Warrant Price resulting from such adjustment and the increase or decrease, if any,
in the number of shares purchasable at such price upon the exercise of a Warrant, setting forth in reasonable detail the method of calculation
and the facts upon which such calculation is based. Upon the occurrence of any event specified in Sections 4.1, 4.2, 4.3 or 4.4, then,
in any such event, the Company shall give written or electronic notice to the Warrant holder, at the last address set forth for such holder
in the Warrant Register, of the record date or the effective date of the event. Failure to give such notice, or any defect therein, shall
not affect the legality or validity of such event.


 


4.6  Form of Warrant. The form of Warrant need
not be changed because of any adjustment pursuant to this Section 4, and Warrants issued after such adjustment may state the same Warrant
Price and the same number of shares as is stated in the Warrants initially issued pursuant to this Agreement. However, the Company may
at any time in its sole discretion make any change in the form of Warrant that the Company may deem appropriate and that does not affect
the substance thereof, and any Warrant thereafter issued or countersigned, whether in exchange or substitution for an outstanding Warrant
or otherwise, may be in the form as so changed.


   


5.   Transfer and Exchange of Warrants.


 


5.1   Registration of Transfer. The Warrant Agent
shall register the transfer, from time to time, of any outstanding Warrant upon the Warrant Register, upon surrender of such Warrant for
transfer, properly endorsed with signatures properly guaranteed and accompanied by appropriate instructions for transfer. Upon any such
transfer, a new Warrant representing an equal aggregate number of Warrants shall be issued and the old Warrant shall be cancelled by the
Warrant Agent. The Warrants so cancelled shall be delivered by the Warrant Agent to the Company from time to time upon request.


  


5.2   Procedure for Surrender of Warrants. Warrants
may be surrendered to the Warrant Agent, together with a written request for exchange, and thereupon the Warrant Agent shall issue in
exchange therefor one or more new Warrants as requested by the registered holder of the Warrants so surrendered, representing an equal
aggregate number of Warrants; provided, however, in the event a Warrant surrendered for transfer bears a restrictive legend, the Warrant
Agent shall not cancel such Warrant and issue new Warrants in exchange therefor until the Warrant Agent has received an opinion of counsel
for the Company stating such transfer may be made and indicating whether the new Warrants must also bear a restrictive legend. Book-entry
held warrants may be surrendered electronically by any means acceptable to the Company.


 


5.3   Fractional Warrants. The Warrant Agent shall
not be required to effect any registration of transfer or exchange which will result in the issuance of a warrant certificate for a fraction
of a warrant.


 


5.4   Service Charges. No service charge shall
be made for any exchange or registration of transfer of Warrants.


 


5.5   Warrant Execution and Countersignature.
The Warrant Agent is hereby authorized to countersign and deliver, in accordance with the terms of this Agreement, the Warrants required
to be issued pursuant to the provisions of this Section 5, and the Company, whenever required by the Warrant Agent, will supply the Warrant
Agent with Warrants duly executed on behalf of the Company for such purpose.


 




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6.   Other Provisions Relating to Rights of Holders
of Warrants.


 


6.1   No Rights as Stockholder. A Warrant does
not entitle the registered holder thereof to any of the rights of a stockholder of the Company, including, without limitation, the right
to receive dividends, or other distributions, exercise any preemptive rights to vote or to consent or to receive notice as stockholders
in respect of the meetings of stockholders or the election of directors of the Company or any other matter.


 


6.2   Lost, Stolen, Mutilated, or Destroyed Warrants.
If any Warrant is lost, stolen, mutilated, or destroyed, the Company and the Warrant Agent may on such terms as to indemnity or otherwise
as they may in their discretion impose (which shall, in the case of a mutilated Warrant, include the surrender thereof), issue a new Warrant
of like denomination, tenor, and date as the Warrant so lost, stolen, mutilated, or destroyed. Any such new Warrant shall constitute a
substitute contractual obligation of the Company, whether or not the allegedly lost, stolen, mutilated, or destroyed Warrant shall be
at any time enforceable by anyone.


 


6.3   Reservation of Common Stock. The Company
shall at all times reserve and keep available a number of its authorized but unissued shares of Common Stock that will be sufficient to
permit the exercise in full of all outstanding Warrants issued pursuant to this Agreement.


   


7.   Concerning the Warrant Agent and Other Matters.


 


7.1   Payment of Taxes. The Company will from
time to time promptly pay all taxes and charges that may be imposed upon the Company or the Warrant Agent in respect of the issuance or
delivery of shares of Common Stock upon the exercise of Warrants, but the Company shall not be obligated to pay any transfer taxes in
respect of the Warrants or such shares.


 


7.2   Resignation, Consolidation, or Merger of Warrant
Agent.


 


7.2.1   Appointment of Successor Warrant Agent.
The Warrant Agent, or any successor to it hereafter appointed, may resign its duties and be discharged from all further duties and liabilities
hereunder after giving sixty (60) days’ notice in writing to the Company. If the office of the Warrant Agent becomes vacant by resignation
or incapacity to act or otherwise, the Company shall appoint in writing a successor Warrant Agent in place of the Warrant Agent. If the
Company shall fail to make such appointment within a period of 30 days after it has been notified in writing of such resignation or incapacity
by the Warrant Agent or by the holder of the Warrant (who shall, with such notice, submit his Warrant for inspection by the Company),
then the holder of any Warrant may apply to a court of competent jurisdiction for the appointment of a successor Warrant Agent. Any successor
Warrant Agent, whether appointed by the Company or by such court, shall be authorized to exercise corporate trust powers and subject to
supervision or examination by federal or state authority. After appointment, any successor Warrant Agent shall be vested with all the
authority, powers, rights, immunities, duties, and obligations of its predecessor Warrant Agent with like effect as if originally named
as Warrant Agent hereunder, without any further act or deed; but if for any reason it becomes necessary or appropriate, the predecessor
Warrant Agent shall execute and deliver, at the expense of the Company, an instrument transferring to such successor Warrant Agent all
the authority, powers, and rights of such predecessor Warrant Agent hereunder; and upon request of any successor Warrant Agent the Company
shall make, execute, acknowledge, and deliver any and all instruments in writing for more fully and effectually vesting in and confirming
to such successor Warrant Agent all such authority, powers, rights, immunities, duties, and obligations.


 




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 7.2.2   Notice of Successor Warrant Agent.
In the event a successor Warrant Agent shall be appointed, the Company shall give notice thereof to the predecessor Warrant Agent and
the transfer agent for the Common Stock not later than the effective date of any such appointment.


 


7.2.3   Merger or Consolidation of Warrant Agent.
Any corporation into which the Warrant Agent may be merged or with which it may be consolidated or any corporation resulting from any
merger or consolidation to which the Warrant Agent shall be a party shall be the successor Warrant Agent under this Agreement without
any further act.


 


7.3   Fees and Expenses of Warrant Agent.


 


7.3.1   Remuneration. The Company agrees to pay
the Warrant Agent reasonable remuneration for its services as such Warrant Agent hereunder as set forth on Exhibit B
hereto, and will reimburse the Warrant Agent upon demand for all expenditures that the Warrant Agent may reasonably incur in the execution
of its duties hereunder.


 


7.3.2   Further Assurances. The Company agrees
to perform, execute, acknowledge, and deliver or cause to be performed, executed, acknowledged, and delivered all such further and other
acts, instruments, and assurances as may reasonably be required by the Warrant Agent for the carrying out or performing of the provisions
of this Warrant Agreement.


 


7.4   Liability of Warrant Agent.


 


7.4.1   Reliance on Company Statement. Whenever
in the performance of its duties under this Agreement, the Warrant Agent shall deem it necessary or desirable that any fact or matter
be proved or established by the Company prior to taking or suffering any action hereunder, such fact or matter (unless other evidence
in respect thereof be herein specifically prescribed) may be deemed to be conclusively proved and established by a statement signed by
the Chief Executive Officer, President, Chief Operating Officer, Chief Financial Officer, Executive Vice President, Treasurer, or Secretary
of the Company and delivered to the Warrant Agent. The Warrant Agent may rely upon such statement for any action taken or suffered in
good faith by it pursuant to the provisions of this Agreement.


  


7.4.2   Indemnity. The Warrant Agent shall be
liable hereunder only for its own gross negligence, willful misconduct or bad faith. The Company agrees to indemnify the Warrant Agent
and save it harmless against any and all liabilities, including judgments, costs and reasonable counsel fees, for anything done or omitted
by the Warrant Agent in the execution of this Agreement except as a result of the Warrant Agent’s gross negligence, willful misconduct,
or bad faith.


 


7.4.3   Exclusions. The Warrant Agent shall have
no responsibility with respect to the validity of this Agreement or with respect to the validity or execution of any Warrant (except its
countersignature thereof); nor shall it be responsible for any breach by the Company of any covenant or condition contained in this Agreement
or in any Warrant; nor shall it be responsible to make any adjustments required under the provisions of Section 4 hereof or responsible
for the manner, method, or amount of any such adjustment or the ascertaining of the existence of facts that would require any such adjustment;
nor shall it by any act hereunder be deemed to make any representation or warranty as to the authorization or reservation of any shares
of Common Stock to be issued pursuant to this Agreement or any Warrant or as to whether any shares of Common Stock will when issued be
valid and fully paid and nonassessable.


 




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7.5   Acceptance of Agency. The Warrant Agent
hereby accepts the agency established by this Agreement and agrees to perform the same upon the terms and conditions herein set forth
and among other things, shall account promptly to the Company with respect to Warrants exercised and concurrently account for, and pay
to the Company, all moneys received by the Warrant Agent for the purchase of shares of the Company’s Common Stock through the exercise
of Warrants.


 


7.6   Waiver. The Warrant Agent hereby waives
any and all right, title, interest or claim of any kind (“Claim”) in or to any distribution of any account in
which funds related to the purchase or exercise of the Warrants are held, and hereby agrees not to seek recourse, reimbursement, payment
or satisfaction for any Claim against any such account for any reason whatsoever.


 


8.   Miscellaneous Provisions.


 


8.1   Successors. All the covenants and provisions
of this Agreement by or for the benefit of the Company or the Warrant Agent shall bind and inure to the benefit of their respective successors
and assigns.


 


8.2   Notices. Any notice or other communication
required or which may be given hereunder shall be in writing and either be delivered personally or by private national courier service,
or be mailed, certified or registered mail, return receipt requested, postage prepaid, and shall be deemed given when so delivered personally
or, if sent by private national courier service, on the next business day after delivery to the courier, or, if mailed, two business days
after the date of mailing, as follows:


 


Zion Oil & Gas, Inc.


12655 North Central Expressway, Suite 1000


Dallas, Texas 75243


Attn:  Corporate Secretary/Treasurer


 


Any notice, statement or demand authorized by this Agreement
to be given or made by the holder of any Warrant or by the Company to or on the Warrant Agent shall be sufficiently given when so delivered
if by hand or overnight delivery or if sent by certified mail or private courier service five days after deposit of such notice, postage
prepaid, addressed (until another address is filed in writing by the Warrant Agent with the Company), as follows:


   


American Stock Transfer & Trust Company, LLC


6201 15th Avenue


Brooklyn, New York 11219


Attn: Account Executive


 


8.3   Applicable Law. The validity, interpretation,
and performance of this Agreement and of the Warrants shall be governed in all respects by the laws of the State of New York, without
giving effect to conflict of laws. Each party hereby agrees that any action, proceeding or claim against it arising out of or relating
in any way to this Agreement shall be brought and enforced in the appropriate state or federal courts in the State of New York, and irrevocably
submits to such jurisdiction, which jurisdiction shall be exclusive. Each party hereby waives any objection to such exclusive jurisdiction
and that such courts represent an inconvenient forum.


 




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8.4   Persons Having Rights under this Warrant Agreement.
Nothing in this Agreement expressed and nothing that may be implied from any of the provisions hereof is intended, or shall be construed,
to confer upon, or give to, any person or corporation other than the parties hereto and the registered holders of the Warrants, any right,
remedy, or claim under or by reason of this Agreement or of any covenant, condition, stipulation, promise, or agreement hereof. All covenants,
conditions, stipulations, promises, and agreements contained in this Agreement shall be for the sole and exclusive benefit of the parties
hereto and their successors and assigns and of the registered holders of the Warrants. 


 


 8.5   Examination of the Warrant Agent Agreement.
A copy of this Agreement shall be available at all reasonable times at the office of the Warrant Agent for inspection by the registered
holder of any Warrant. The Warrant Agent may require any such holder to submit his Warrant for inspection by it.


 


8.6   Counterparts. This Agreement may be executed
in any number of 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.


 


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


 


8.8   Amendments. This Agreement may be amended
by the parties hereto without the consent of any registered holder for the purpose of curing any ambiguity, or of curing, correcting or
supplementing any defective provision contained herein or adding or changing any other provisions, including the shortening of the Exercise
Period pursuant to Section 3.2, with respect to matters or questions arising under this Agreement as the parties may deem necessary or
desirable and that the parties deem shall not adversely affect the interest of the registered holders. All other modifications or amendments,
including any amendment to increase the Warrant Price, shall require the written consent of a majority of the then outstanding Warrants.
Notwithstanding the foregoing, the Company may lower the Warrant Price or extend or reduce the duration of the Exercise Period in accordance
with Sections 3.1 and 3.2, respectively, without such consent.


 


8.9   Severability. This 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
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 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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IN WITNESS WHEREOF, this Agreement has been duly executed
by the parties hereto effective as of the day and year first above written.


 


	ZION
    OIL & GAS, INC.	 
	 	 	 
	By:	/s/Martin
    M. van Brauman	 
	 	 	 
	Name: 	Martin M. van Brauman	 
	Title:	Corporate Secretary, Treasurer, EVP,
    Director	 
	 	 	 
	Date:	4/8/2021	 
	 	 
	AMERICAN STOCK TRANSFER
    & TRUST COMPANY, LLC
	 	 	 
	By:	/s/Michael
    Nespoli	 
	 	 	 
	Name:	Michael Nespoli	 
	Title:	Executive Director	 
	 	Relationship Management	 
	 	 	 
	Date:	4/8/2021	 


 




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Exhibit A


 


[Face of Certificate - ZION OIL & GAS, INC.]


 


(SEE REVERSE SIDE FOR LEGEND)


 


W


 


WARRANTS


 


(THIS WARRANT WILL BE VOID IF NOT EXERCISED PRIOR TO 5:00 P.M.,
EASTERN STANDARD TIME, June 12, 2023)


 


ZION OIL & GAS, INC.


 


CUSIP 989696 315


 


WARRANT


 


THIS CERTIFIES THAT, for value received _____________ is the
registered holder of a Warrant or Warrants expiring June 12, 2023 (the “Warrant”) to purchase for each Warrant one fully paid
and non-assessable share of Common Stock, par value $.01 per share (the “Shares”), of ZION OIL & GAS, INC., a Delaware
corporation (the “Company”). Each Warrant entitles the holder thereof to purchase from the Company, commencing on June 11,
2021, one Share of the Company at the price of $0.25 per share, upon surrender of this Warrant Certificate and payment of the Warrant
Price at the office or agency of the Warrant Agent, American Stock Transfer & Trust Company, LLC (such surrender may be made by electronic
means and such payment by check or by electronic means made payable to the order of the Company), but only subject to the conditions set
forth herein and in the Warrant Agent Agreement between the Company and the Warrant Agent. In no event shall the registered holder of
this Warrant be entitled to receive a net-cash settlement or other consideration in lieu of physical settlement in Shares of the Company.
The Warrant Agent Agreement provides that, upon the occurrence of certain events, the Warrant Price, the Exercise Period and the number
of Warrant Shares purchasable hereunder, set forth on the face hereof, may, subject to certain conditions, be adjusted. The term Warrant
Price as used in this Warrant Certificate refers to the price per Share at which Shares may be purchased at the time the Warrant is exercised.


 


This Warrant may expire on the date first above written, if
it is not exercised prior to such date by the registered holder pursuant to the terms of the Warrant Agent Agreement. The Company in its
sole discretion may extend the duration of the Unit Option under the Unit Program, which would extend the Warrant Exercise Period by the
same extension of days.


 


Upon any exercise of the Warrant for less than the total number
of full Shares provided for herein, there shall be issued to the registered holder hereof or his/her/its assignee a new Warrant Certificate
covering the number of Shares for which the Warrant has not been exercised.


 


Warrant Certificates, when surrendered at the office or agency
of the Warrant Agent or by any electronic means to the Company by the registered holder hereof in person or by attorney duly authorized
in writing, may be exchanged in the manner and subject to the limitations provided in the Warrant Agent Agreement, but without payment
of any service charge, for another Warrant Certificate or Warrant Certificates of like tenor and evidencing in the aggregate a like number
of Warrants.


 




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Upon due presentment by electronic means or other approved
delivery for registration of transfer of the Warrant Certificate at the office or agency of the Warrant Agent, a new Warrant Certificate
or Warrant Certificates of like tenor and evidencing in the aggregate a like number of Warrants shall be issued to the transferee in exchange
for this Warrant Certificate, subject to the limitations provided in the Warrant Agent Agreement, without charge except for any applicable
tax or other governmental charge.


 


The Company and the Warrant Agent may deem and treat the registered
holder as the absolute owner of the Warrants represented by this Warrant Certificate (notwithstanding any notation of ownership or other
writing hereon made by anyone) for the purpose of any exercise hereof, of any distribution to the registered holder, and for all other
purposes, and neither the Company nor the Warrant Agent shall be affected by any notice to the contrary.


 


This Warrant does not entitle the registered holder to any
of the rights of a stockholder of the Company.


 


COUNTERSIGNED:


American Stock Transfer & Trust Company, LLC


 


WARRANT AGENT


BY:


AUTHORIZED OFFICER


 


DATED:


 


(Signature)


CHIEF EXECUTIVE OFFICER


 


(Seal)


 


(Signature)


SECRETARY


 


 


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