Exhibit 4.2 


 





 


SUBSCRIPTION AGENT AGREEMENT


 


This SUBSCRIPTION AGENT AGREEMENT (this “Agreement”)
is entered into as of March 16, 2018, by and between American Stock Transfer & Trust Company, LLC (the “Subscription Agent”)
and Zion Oil & Gas, Inc. (the “Company”).


 


		1.	The Company is offering (the “Rights Offering”)
to the holders of shares of its common stock, par value $0.01 per share (“Common Stock”), on March 12, 2018 (the “Record
Date”), the Subscription Rights to purchase Rights (“Rights”), each Right consisting of one (1) share of its Common
Stock and one (1) Common Stock Purchase Warrant to purchase an additional one (1) share of Common Stock at a Warrant exercise
price of $3.00. The Warrants will be exercisable on June 29, 2018 and continue to be exercisable for one (1) year after the exercise
date. Except as set forth in Section 8 below, Subscription Rights shall cease to be exercisable at 5:00 P.M., New York City time,
on May 31, 2018 or such later date of which the Company notifies the Subscription Agent orally and confirms in writing (the “Expiration
Date”). The shares of Common Stock will be issuable and tradable as soon as practical by the Subscription Agent after the
close of the Rights Offering on the Expiration Date. One (1) Right is being issued for each 10 shares of Common Stock held on
the Record Date. One (1) Right and payment in full of the subscription price of $5.00 (the “Subscription Price”) are
required to subscribe for one Right. Rights are evidenced by transferable subscription certificates in registered form (“Subscription
Certificates”). Each holder of Subscription Certificate(s) who exercises the holder’s right to subscribe for all Rights that
can be subscribed for with the Rights evidenced by such Subscription Certificate(s) (the “Basic Subscription Right”)
will have the right to subscribe for additional Rights, if any, available as a result of any unexercised Rights (such additional
subscription right being referred to hereafter as the “Additional Subscription Privileged”). The Rights Offering will
be conducted in the manner and upon the terms set forth in the Company’s Prospectus Supplement dated April 2, 2018 (the “Prospectus”).



 


		2.	The Subscription Agent is hereby appointed to affect the
Rights Offering as set forth herein. The Subscription Agent may rely on, and shall be protected in acting upon, any certificate,
instrument, opinion, representation, notice letter or other document delivered to it and believed by it to be genuine and to have
been signed by the proper party or parties.



 


		3.	Enclosed herewith are the following, the receipt of which
the Subscription Agent acknowledges by its execution hereof:



 


		(a)	a copy of the Prospectus Supplement;



 


		(b)	the form of Subscription Certificate (with instructions);



 




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		(c)	resolutions adopted by the
board of directors of the Company in connection with the Rights Offering, certified by the secretary of the Company; and



 


		(d)	notice of guaranteed delivery (“Notice of Guaranteed
Delivery”).



 


		4.	As soon as is reasonably practical, the Subscription Agent
shall mail or cause to be mailed to each holder of Common Stock at the close of business on the Record Date a Subscription Certificate
evidencing the Rights to which such holder is entitled, a Notice of Guaranteed Delivery, a Prospectus and an envelope addressed
to the Subscription Agent. Prior to mailing, the Company shall provide the Subscription Agent with blank Subscription Certificates
which the Subscription Agent shall prepare and issue in the names of holders of Common Stock of record at the close of business
on the Record Date and for the number of Rights to which they are entitled. The Company shall also provide the Subscription Agent
with a sufficient number of copies of each of the documents to be mailed with the Subscription Certificates.



 


		5.	Subscription Procedure.



 


		(a)	Upon the Subscription Agent’s receipt prior to 5:00 P.M.,
New York City time, on the Expiration Date (by mail or delivery) of (ii) any Subscription Certificate completed and endorsed for
exercise, as provided on the reverse side of the Subscription Certificate (except as provided in Section 8 hereof), and (ii) payment
in full of the Subscription Price in U.S. funds by check or bank draft payable (without deduction for bank service charges or
otherwise) to the order of “American Stock Transfer & Trust Company, LLC” the Subscription Agent shall as soon as
practicable after the Expiration Date, but after performing the procedures described in subsections (b) and (c) below, mail to
the subscriber’s registered address on the books of the Company certificates representing the securities underlying each Right
duly subscribed for (pursuant to the Basic Subscription Right and the Additional Subscription Privilege) and furnish a list of
all such information to the Company.



 


		(b)	As soon as practicable after the Expiration Date the Subscription
Agent shall calculate the number of Rights to which each subscriber is entitled pursuant to the Additional Subscription Privilege.
The Additional Subscription Privilege may only be exercised by holders who subscribe to all the Rights that can be subscribed
for under the Basic Subscription Right. The Rights available for additional subscriptions will be those that have not been subscribed
and paid for pursuant to the Basic Subscription Right (the “Remaining Rights”). Where there are sufficient Remaining
Rights to satisfy all additional subscriptions by holders exercising their rights under the Additional Subscription Privilege,
each holder shall be allotted the number of Additional Rights subscribed for. If the aggregate number of Rights subscribed for
under the Additional Subscription Privilege exceeds the number of Remaining Rights, the number of Remaining Rights allotted to
each participant in the Additional Subscription Privilege shall be the product (disregarding fractions) obtained by multiplying
the number of Remaining Rights by a fraction of which the numerator is the number of Rights subscribed
for by that participant under the Additional Subscription Privilege and the denominator is the aggregate number of Remaining Rights
subscribed for by all participants under the Additional Subscription Privilege. Any fractional Right to which persons exercising
their Additional Subscription Privilege would otherwise be entitled pursuant to such allocation shall be rounded to the next whole
Right.



 






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		(c)	Upon calculating the number of Rights to which each subscriber
is entitled pursuant to the Additional Subscription Privilege and the amount overpaid, if any, by each subscriber, the Subscription
Agent shall, as soon as practicable, furnish a list of all such information to the Company.



 


		(d)	Upon calculating the number of Rights to which each subscriber
is entitled pursuant to the Additional Subscription Privilege and assuming payment for the additional Rights subscribed for has
been delivered, the Subscription Agent shall mail, as contemplated in subsection (a) above, the certificates representing the
additional securities which the subscriber has been allotted. If a lesser number of Rights is allotted to a subscriber under the
Additional Subscription Privilege than the subscriber has tendered payment for, the Subscription Agent shall remit the difference
to the subscriber without interest or deduction at the same time as certificates representing the securities allotted pursuant
to the Additional Subscription Privilege are mailed.



 


		(e)	Funds received by the Subscription Agent pursuant to the
Basic Subscription Right and the Additional Subscription Privilege shall be held by it in a segregated account. Upon mailing certificates
representing the securities and refunding subscribers for additional Rights subscribed for but not allocated, if any, the Subscription
Agent shall promptly remit to the Company all funds received in payment of the Subscription Price for Rights issued in the Rights
Offering. The Subscription Agent will not be obligated to calculate or pay interest to any holder or party.



 


		6.	Until 5:00 P.M., New York City time, on the third Business
Day (as defined below) prior to the Expiration Date, the Subscription Agent shall facilitate subdivision or transfers of Subscription
Certificates by issuing new Subscription Certificates in accordance with the instructions set forth on the reverse side of the
Subscription Certificates. As used in herein, “Business Day” shall mean any day other than a Saturday, a Sunday, or
a day on which banking institutions in the State of New York are authorized or obligated by law or executive order to close.



 


		7.	The Company shall have the absolute right to reject any
defective exercise of Rights or to waive any defect in exercise. Unless requested to do so by the Company, the Subscription Agent
shall not be under any duty to give notification to holders of Subscription Certificates of any defects or irregularities in subscriptions.
Subscriptions will not be deemed to have been made until any such defects or irregularities have been cured or waived within such
time as the Company shall determine. The Subscription Agent shall as soon as practicable return
Subscription Certificates with the defects or irregularities which have not been cured or waived to the holder of the Rights.
If any Subscription Certificate is alleged to have been lost, stolen or destroyed, the Subscription Agent should follow the same
procedures followed for lost stock certificates representing Common Stock it uses in its capacity as transfer agent for the Company’s
Common Stock.



 






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		8.	If prior to 5:00 P.M., New York City time, on the Expiration
Date the Subscription Agent receives (i) payment in full of the Subscription Price for the Rights being subscribed for and (ii)
a guarantee notice substantially in the form of the notice of guaranteed delivery (“Notice of Guaranteed Delivery”)
delivered with the Subscription Certificate, from a financial institution having an office or correspondent in the United States,
or a member firm of any registered United States national securities exchange or of FINRA stating the certificate number of the
Subscription Certificate relating to the Rights, the name and address of the exercising subscriber, the number of Rights represented
by the Subscription Certificate held by such exercising subscriber, the number of Rights being subscribed for pursuant to the
Subscription Rights and guaranteeing the delivery to the Subscription Agent of the Subscription Certificate evidencing such Rights
within two (2) NASDAQ trading days (“Trading Days”) following the date of the Notice of Guaranteed Delivery, then the
Rights may be exercised even though the Subscription Certificate was not delivered to the Subscription Agent prior to 5:00 P.M.,
New York City time, on the Expiration Date, provided that within two (2) Trading Days following the date of the Notice of Guaranteed
Delivery the Subscription Agent receive the properly completed Subscription Certificate evidencing the Rights being exercised,
with signatures guaranteed if required.



 


		9.	The Subscription Agent shall deliver to the Company copies
of the exercised Subscription Certificates in accordance with written directions received from the Company. The Subscription Agent
shall deliver to the subscribers who have duly exercised Rights, at their registered addresses certificates representing the securities
subscribed for as instructed on the reverse side of the Subscription Certificates.



 


		10.	The Subscription Agent shall notify the Company by telephone
on or before the close of business on each Business Day during the period commencing five (5) Business Days after the mailing
of the Rights and ending at the Expiration Date (and in the case of guaranteed deliveries ending two (2) Trading Days after the
Expiration Date) (a “daily notice”), which notice shall thereafter be confirmed in writing, of (i) the number of Rights
exercised on the day covered by such daily notice, (ii) the number of Rights subject to guaranteed exercises on the day covered
by such daily notice, (iii) the number of Rights for which defective exercises have been received on the day covered by such daily
notice, and (iv) the cumulative total of the information set forth in clauses (i) through (iii) above. At or before 5:00 P.M.,
New York City time, on the first Trading Day following the Expiration Date the Subscription Agent shall certify in writing to
the Company the cumulative total through the Expiration Date of all the information set forth in clauses (i) through (iii) above.
At or before 10:00 A.M., New York City time, on the fifth Trading Day following the Expiration Date the Subscription Agent will
execute and deliver to the Company a certificate setting forth the number of Rights exercised pursuant
to a Notice of Guaranteed Delivery and as to which Subscription Certificates have been timely received. The Subscription Agent
shall also maintain and update a listing of holders who have fully or partially exercised their Rights and holders who have not
exercised their Rights. The Subscription Agent shall provide the Company or its designees with such information compiled by the
Subscription Agent pursuant to this Section 10 as part of the daily notice to the Company.



 






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		11.	With respect to notices or instructions to be provided
by the Company hereunder, the Subscription Agent may rely and act on any written instruction signed by any one or more of the
following authorized officers or employees of the Company:



 


	 	Name	 	Title
	 	Martin M. van Brauman	 	Treasurer/Secretary
	 	Mike Croswell	 	CFO


 


		12.	Whether or not the Rights Offering is consummated, the
Company agrees to pay the Subscription Agent for services rendered hereunder, as set forth in the schedule attached to this Agreement.



 


		13.	The Subscription Agent may employ or retain such agents
(including but not limited to, vendors, advisors and subcontractors) as it reasonably requires to perform its duties and obligations
hereunder; may pay reasonable remuneration for all services so performed by such agents; shall not be responsible for any misconduct
on the part of such agents; and in the case of counsel, may rely on the written advice or opinion of such counsel, which shall
be full and complete authorization and protection in respect of any action taken, suffered or omitted by the Subscription Agent
hereunder in good faith and in accordance with such advice or opinion. Additionally, the Subscription Agent shall identify, report
and deliver any unclaimed property and/or payments to all states and jurisdictions for the Company in accordance with applicable
abandoned property law. The Subscription Agent shall also provide information agent services to the Company on terms to be mutually
agreed upon by the parties hereto.



 


		14.	The Company hereby covenants and agrees to indemnify, reimburse
and hold the Subscription Agent and its officers, directors, employees and agents harmless against any loss, liability or reasonable
expense (including legal and other fees and expenses) incurred by the Subscription Agent arising out of or in connection with
entering into this Agreement or the performance of its duties hereunder, except for such losses, liabilities or expenses incurred
as a result of its gross negligence, bad faith or willful misconduct. The Company shall not be liable under this indemnity with
respect to any claim against the Subscription Agent unless the Company is notified of the written assertion of a claim against
it, or of any action commenced against it, promptly after it shall have received any such written information as to the nature
and basis of the claim; provided, however, that failure by the Subscription Agent to provide such notice shall not relieve the
Company of any liability hereunder if no prejudice occurs.



 




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In no event shall the Subscription Agent have any liability for any incidental,
special, statutory, indirect or consequential damages, or for any loss of profits, revenue, data or cost of cover.


 


All provisions regarding indemnification, liability and limits
thereon shall survive the resignation or removal of the Subscription Agent or the termination of this Agreement.


 


		15.	Any notice or communication by the Subscription Agent or
the Company to the other is duly given if in writing and delivered in person or via first class mail (postage prepaid), or overnight
air courier to the other’s address.



 


If to the Company:


 


12655 North Central Expressway


Suite 1000


Dallas, Texas 75243


Attn: Mike Croswell, CFO


Tel: (214) 221-4610


 


If to the Subscription Agent:


 


American Stock Transfer & Trust Company, LLC


6201 15th Avenue


Brooklyn, New York 11219


Attn: Corporate Actions


Tel: (718) 921.8200


 


with copy to:


 


American Stock Transfer & Trust Company, LLC


6201 15th Avenue


Brooklyn, New York 11219


Attn: General Counsel


Tel: (718) 921.8200


 


The Subscription Agent and the Company may, by notice to the
other, designate additional or different addresses for subsequent notices or communications.


 


		16.	If any provision of this Agreement shall be held illegal,
invalid, or unenforceable by any court, this Agreement shall be construed and enforced as if such provision had not been contained
herein and shall be deemed an Agreement between us to the full extent permitted by applicable law.



 


		17.	This Agreement shall be governed by and construed in accordance
with the laws of the State of New York, without giving effect to principles of conflicts of law, and shall inure to the benefit
of and be binding upon the successors and permitted assigns of the parties hereto.



 


		18.	Neither this Agreement, nor any rights or obligations hereunder,
may be assigned by either party without the written consent of the other party. However, the Subscription Agent may assign this
Agreement or any rights granted hereunder, in whole or in part, either to affiliates, another division, subsidiaries or in connection
with its reorganization or to successors of all or a majority of the Subscription Agent’s assets or business without the prior
written consent of the Company.



 


		19.	No provision of this Agreement may be amended, modified
or waived, except in writing signed by all of the parties hereto. This Agreement may be executed in counterparts, each of which
shall be for all purposes deemed an original, but all of which together shall constitute one and the same instrument.



 


		20.	Nothing herein contained shall amend, replace or supersede
any agreement between the Company and the Subscription Agent to act as the Company’s transfer agent, which agreement shall remain
of full force and effect.



 


[signature page follows]


 




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This Subscription Agent Agreement
has been executed by the parties hereto as of the date first written above.


 


	 	ZION OIL & GAS, INC.
	 	 	 
	 	By:	/s/ Martin M. van Brauman
	 	 	Name:	Martin M. van Brauman
	 	 	Title:	Secretary/Treasurer/SVP Director


 


Agreed & Accepted:


 


	AMERICAN STOCK TRANSFER & TRUST COMPANY. LLC	 
	 	 	 	 
	By:	/s/ Michael Legregin	 
	 	Name:	Michael Legregin	 
	 	Title:	SVP	 


 




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Fee Schedule


 


Project fee of $65,000.00.


Per DTC or registered holder Tender Fee $10.00


Plus out-of-pocket
and extraordinary expenses


 


DTC new cusip eligibility fee $1,000.00 (Non-Negotiable)


 


Additional fee of $2,500.00 for each extension of the Rights
Offering, plus reasonable out-of-pocket expenses associated with such extension.


 


See attached Proposal For: Corporate Action Services, dated
March 12, 2018.


 


Fees are payable prior to the Launch date


 


Santander Bank NA.


601 Penn Street


Reading, PA 19601


 


ABA # 231372691


SWIFT CODE: SVRNUS33


For further credit to: American Stock Transfer & Trust,
LLC


6201 15TH Avenue


Brooklyn, NY 11219


Account # 3036002123


Reference: Zion Oil & Gas, Inc.


Attn: Accounts Receivable


 


The party below is responsible for payment of the fees:


 


Name: Zion Oil & Gas, Inc.


Attention: Mike Croswell


Address: 12655 North Central Expressway


Address: Suite 1000


Address: Dallas, Texas 75243


Facsimile: (214) 221-6510


Phone: (214) 221-4610


Email: mike.croswell@zionoil.com


 


The fees quoted in this schedule apply to services
ordinarily rendered by American Stock Transfer & Trust Company, LLC (“AST”) as Subscription Agent and are
subject to adjustment based on final review of documents, or when AST is called upon to undertake unusual duties or
responsibilities, or as changes in law, procedures, or the cost of doing business demand. Out-of-pocket expenses include, but
are not limited to, 1099’s (calculations, production, print, mail, and IRS reporting), cost basis calculations and
reporting, and regulatory mailings. Furthermore, the fees quoted in this schedule are based upon information provided to AST
and are subject to change upon modification or supplementation of such information resulting in the provision of additional
services by AST. Services in addition to and not contemplated in this Agreement, including, but not limited to, document
amendments and revisions, calculations, notices and reports, legal fees and unanticipated
transaction costs (including charges for wire transfers, checks, internal transfers and securities transactions) will be
billed as extraordinary expenses.




 






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