<PAGE>   1
                                                                 Exhibit 10.3(b)


                     RETIREMENT AND NONCOMPETITION AGREEMENT

         This Retirement and Noncompetition Agreement (this "AGREEMENT") is
entered into as of May __, 1999, by and between Belden & Blake Corporation, an
Ohio corporation (the "COMPANY") and Ronald L. Clements, a natural person
("CLEMENTS") and, with respect to SECTION 8 only, TPG Partners II, L.P. ("TPG").

                                    RECITALS

         A. Clements is currently serving as the Chief Executive Officer of the
Company and is a member of the Board of Directors of the Company.

         B. Clements desires to retire from his employment with the Company and
from his positions as an officer and a director of the Company.

         C. The parties desire to enter into this Agreement to establish certain
terms under which Clements is leaving the Company.

         NOW, THEREFORE, in consideration of the premises set forth above and
the covenants contained in this Agreement and for other good and valuable
consideration, the receipt and adequacy of which are hereby acknowledged by the
parties, the parties hereby agree as follows:

                                    AGREEMENT

         1. RETIREMENT DATE. Clements' retirement from his positions as an
officer and a director of the Company and any other positions with the Company
or any employee benefit plan or trust of the Company shall be effective as of
the earlier of (i) the date upon which a new Chief Executive Officer commences
employment with the Company, and (ii) June 30, 1999 (the "RETIREMENT DATE").
Notwithstanding the foregoing, Clements' employment with the Company shall
terminate on June 30, 1999 (the "EFFECTIVE DATE").

         2. NONCOMPETITION PAYMENT.

                  (a) PAYMENT. In consideration for Clements' undertaking in
accordance with this Agreement, the Company shall pay to Clements a payment of
Seven Hundred Twenty-Five Thousand Dollars ($725,000) (the "NONCOMPETITION
PAYMENT"). The Noncompetition Payment shall be paid in three installments. The
first installment of Three Hundred Fifty Thousand Dollars ($350,000) shall be
paid on July 1, 1999. The second installment of Two Hundred Fifty Thousand
Dollars ($250,000) shall be paid on January 3, 2000. The third installment of
One Hundred Twenty-Five Thousand Dollars ($125,000) shall be paid on July 1,
2000. The Company will issue an IRS Form 1099 with respect to the Noncompetition
Payment.

                  (b) INDEMNIFICATION. Clements agrees that he will be solely
responsible for all state and federal taxes, if any, associated with the
Noncompetition Payment, and Clements agrees to indemnify the Company for, and to
hold it harmless from, any liability, taxes, penalties,


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costs or attorneys' fees it may incur in connection with any failure to withhold
any tax, social security, FICA or any other amounts associated with the
Noncompetition Payment to Clements.

         3.       RETIREMENT PAYMENTS AND BENEFITS.

                  (a)      SALARY PAYMENT.

                           (i) Regardless of whether the Retirement Date is
earlier than the Effective Date, Clements shall continue to earn and the Company
shall continue to pay to Clements the prorated amount of his current annual base
salary through the Effective Date (the "SALARY PAYMENT"). The Salary Payment
shall be paid to Clements at the Company's regular payroll intervals.

                           (ii) Clements acknowledges that he is responsible for
paying any and all taxes relating to the Salary Payment. Notwithstanding the
foregoing, in its discretion, the Company may withhold from the Salary Payment
federal, state and other income taxes required to be withheld or paid under
applicable law, and deduct appropriate amounts as may be required by applicable
law.

                  (b) HEALTH CARE BENEFITS. Clements shall be eligible to
continue to participate, at his current participation and contribution levels,
in the Company's health care programs during the two-year period beginning on
the Effective Date and ending on the second anniversary of the Effective Date.

                  (c) CLUB MEMBERSHIP. The Company shall pay, on behalf of
Clements, Clements' monthly club membership dues to Glenmoor Country Club that
become due and payable during the period beginning on the Effective Date and
ending on the second anniversary of the Effective Date. The Company agrees that
it shall not terminate Clements' membership to Glenmoor County Club prior to the
second anniversary of the Effective Date.

                  (d) DEFERRED STOCK BONUS PROGRAM. In accordance with Section
6(a) of that certain Belden & Blake Corporation Deferred Stock Bonus Program,
upon the Effective Date, the Company shall exercise its option to cause the
trustee to deliver to Clements within thirty (30) days of the Effective Date one
or more stock certificates for the number of shares of common stock of the
Company credited to Clements' Deferred Share Bonus Account. The parties agree
that there are 4,345 shares of common stock in Clements' Deferred Stock Bonus
Account.

                  (e) NO OTHER PAYMENTS. Clements agrees and acknowledges that
the foregoing payments and benefits described in this SECTION 3 and the
Noncompetition Payment are the only amounts which he shall receive or be
entitled to receive as of the Effective Date, and he waives any and all claims
he may have to any other payments or benefits including, but not limited to,
salary, wages, bonus or any other form of incentive or severance pay. More
specifically, Clements agrees and acknowledges that by virtue of his decision to
retire voluntarily, he is not entitled to any benefits or pay pursuant to any
employment agreement between Clements and the Company, or the Severance
Agreement dated as of October 25, 1996



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between Clements and the Company, or pursuant to any other severance agreement
or arrangement.

         4. 1997 OPTIONS. The following options (the "1997 OPTIONS") granted to
Clements under the Belden & Blake Corporation Stock Option Plan pursuant to the
Nonqualified Stock Option Agreement dated June 27, 1997 (the "NONQUALIFIED
OPTION AGREEMENT") are currently outstanding:
<TABLE>
<CAPTION>

                              Number of Shares of
                                 Common Stock
       Date of Grant           Underlying Option        Exercise Price           Vesting Schedule
       -------------           -----------------        --------------           ----------------

<S>                              <C>                     <C>             <C>
          6/27/97                   137,366                 $10.82             Options vest and are
                                                                            exercisable as to 34,341.5
                                                                            shares on 6/27/98 and as to
                                                                             an additional 8,585.38 on
                                                                           each three month anniversary
                                                                                    thereafter
</TABLE>

         5. ROLLOVER OPTIONS. The following options (the "ROLLOVER OPTIONS")
granted to Clements under the Belden & Blake Corporation Stock Option Plan
pursuant to the Employee Stock Option Agreements dated May 28, 1994, August 24,
1995 and August 26, 1996 all of which are amended by that certain letter
agreement dated June 27, 1997 by and between the Company and Clements
(collectively, the "ROLLOVER STOCK OPTION AGREEMENTS") are currently
outstanding:

            Number of Shares of
         Common Stock UNDERLYING
                  Option               Exercise Price           Vesting Schedule
                  ------               --------------           ----------------

                  31,168                   $0.10                  Fully Vested

         6. ADDITIONAL STOCK OPTIONS. Clements does not own any options to
purchase shares of common stock of the Company other than the 1997 Options and
the Rollover Options.

         7. OPTION PUT. The parties agree and acknowledge that (i) the Option
Put set forth in Section 11 of the Rollover Stock Option Agreements pertains
only to the Rollover Options and is not amended or terminated hereby and (ii)
the 1997 Options do not contain an option put or any other right to require the
Company to repurchase from Clements the 1997 Options.

         8.       TAG-ALONG RIGHT OF CLEMENTS.

                  (a) PROPOSAL. Subject to SECTION 8(c) hereof, if TPG proposes
to sell seventy-five percent (75%) or more of its holdings of the Company's
common stock, on a fully-diluted, fully-converted basis, to a third-party
offeror (a "PROPOSAL"), TPG shall deliver a notice (the "TAG-ALONG NOTICE") with
respect to such Proposal to Clements summarizing the



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pertinent information about the Proposal, including the purchase price (the
"TAG-ALONG PRICE"), together with a copy of any writing between TPG and the
third party offeror necessary to establish the terms of such Proposal.

                  (b) ELECTION NOTICE. Clements shall have a period of ten (10)
business days after delivery of the Tag-Along Notice within which to deliver
written notice (the "ELECTION NOTICE") to TPG of Clements' desire to participate
in the transaction described in the Proposal, in which event Clements will be
entitled to sell to the third party offeror up to the number of shares he owns
beneficially as a result of an exercise of any or all of his vested 1997 Options
or is entitled to receive upon exercise of his vested 1997 Options.

                  If Clements delivers the Election Notice to TPG within such
ten (10) business day period he shall be obligated to sell the amount of shares
designated in such Election Notice to the third party offeror pursuant to the
terms and conditions of the Proposal, and the number of shares to be sold by TPG
may be reduced accordingly.

                  (c)      LIMITATIONS ON TAG-ALONG RIGHT.

                           (i) Notwithstanding anything herein to the contrary,
Clements may not elect to have any shares included in such sale (1) if the
exercise of his Tag-Along Right would result in a sale by TPG of less than
seventy-five percent (75%) of its holdings of Company common stock, on a
fully-diluted, fully-converted basis, to a third-party offeror, and (2) unless
he takes all actions as the third party offeror shall reasonably request to vest
in the third party offeror title to such shares free and clear of all liens,
charges and encumbrances of any kind.

                           (ii) Clements' Tag-Along Right described in this
SECTION 8 is a one-time right only and such right shall be extinguished upon the
earlier of (1) Clements' participation in a sale described in a Proposal or (2)
Clements' failure to deliver an Election Notice within ten (10) business days of
receiving a Proposal from TPG. TPG's obligations with respect to the delivery of
a Tag-Along Notice to Clements shall terminate upon the extinguishment of
Clements' Tag-Along Right pursuant to this Section 8(c)(ii).

         9. EMPLOYMENT AGREEMENT. That certain Employment Agreement dated as of
June 27, 1997 (the "EMPLOYMENT AGREEMENT") by and between the Company and
Clements is hereby amended to delete Section 4(c) (Purchase Rights) in its
entirety.

         10. INTERESTS IN 401(k) PLAN AND DEFERRED COMPENSATION PLAN. Clements
may continue to hold contributions made by him or on his behalf in the Belden &
Blake 401(k) Profit Sharing Plan and pursuant to the Nonqualified Voluntary
Deferred Compensation Agreement dated as of November 30, 1994 by and between
Clements and the Company as amended by that certain Amendment dated as of May
24, 1999 by and between Clements and the Company (the "DEFERRED COMPENSATION
PLAN"), subject to the express provisions of such plans.

         11.      COVENANTS OF CLEMENTS.



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                  (a) NON-COMPETITION. For a period (the "COVENANT PERIOD"),
commencing on the Effective Date and ending on the second anniversary of the
Effective Date, Clements will not, directly or indirectly:

                           (i) invest in (other than as a passive investor in
securities of a publicly traded entity whose holdings therein do not exceed 5%
of such securities outstanding or in real estate), engage in or be associated
with as a consultant, employer, employee, agent, director, stockholder, partner,
financial backer, affiliate or otherwise, the ownership or operation of any
enterprise relating to the exploration, drilling and/or production of oil and/or
gas in the Appalachian, Michigan and/or Illinois basins; provided, however, that
if the agreement contained in this subsection 10(a)(i) is more restrictive than
permitted by the law in the jurisdiction in which the enforcement of this
Agreement is sought, such agreement shall be limited to the extent limited by
law; or

                           (ii) employ, solicit for employment, or endeavor in
any way to entice away from employment by the Company or any of its affiliates,
any person who is employed on the date hereof or during the Covenant Period by
any of them, or (ii) engage, solicit for engagement, or endeavor in any way to
entice away from the engagement of the Company or any of its affiliates any
client or potential client of the Company on the date hereof or during the
Covenant Period.

                  (b) TRADE SECRETS. Clements will not use or disclose any Trade
Secrets (as defined under applicable law) of the Company, its parent or any of
their respective subsidiaries, for so long as the pertinent information or data
remain Trade Secrets, whether or not the Trade Secrets are in written or
tangible form.

         12.      RELEASE.

                  (a) RELEASE. As consideration for the payments and benefits
described herein, Clements hereby releases the Company and its predecessors,
successors, affiliates and their respective officers, directors, employees,
agents, shareholders, attorneys, representatives and assigns from any and all
claims or lawsuits (including, for example, but without limitation, equal
employment claims, wrongful discharge claims, breach of contract and tort
claims, and claims under the Age Discrimination in Employment Act) he may have
that are based on employment of Clements by the Company, the termination of such
employment, or on any other event or omission occurring prior to the date of
this Agreement.

                  (b) CIVIL CODE SECTION 1542. Clements waives any and all
rights he may have under California Civil Code Section 1542 or any other
comparable provision of state or federal law. Section 1542 provides as follows:

         A GENERAL RELEASE DOES NOT EXTEND TO CLAIMS WHICH THE CREDITOR DOES NOT
KNOW OR SUSPECT TO EXIST IN HIS FAVOR AT THE TIME OF EXECUTING THE RELEASE,
WHICH IF KNOWN BY HIM MUST HAVE MATERIALLY AFFECTED HIS SETTLEMENT WITH THE
DEBTOR.



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<PAGE>   6

         Notwithstanding the provisions of Section 1542, and for the purpose of
implementing a full and complete release and discharge of all claims, Clements
expressly acknowledges that this release is intended to include all claims which
Clements does not know or suspect to exist in his favor at this time, and that
this release contemplates extinguishment of such claims.

         13.      MISCELLANEOUS.

                  (a) GOVERNING LAW. This Agreement shall be governed by the
laws of the State of Ohio, without regard to conflict of laws principles.

                  (b) MODIFICATIONS AND AMENDMENTS. This Agreement may not be
modified, changed or supplemented, nor may any obligations hereunder be waived,
except by written instrument signed by the party to be charged.

                  (c) ENTIRE AGREEMENT. This Agreement sets forth the entire
agreement between the parties with respect to the subject matter hereof and,
with the exception of the Employment Agreement (as amended hereby), the
Nonqualified Option Agreement, the Rollover Stock Option Agreements, the
Deferred Compensation Plan, each of which shall remain in full force and effect,
supersedes all prior written or oral and all contemporaneous oral agreements,
statements and understandings by and between the Company and Clements. Clements
acknowledges that he is not relying on any statement or representation of the
Company or Texas Pacific Group, or their respective employees or agents with
respect to the subject matter, basis or effect of this Agreement.

                  (d) SEVERABILITY. In the event that any provision of this
Agreement is found to be excessive in scope or otherwise invalid or
unenforceable, such provision shall be adjusted rather than voided, if possible,
so that it is enforceable to the maximum extent possible, and all other
provisions of this Agreement shall be deemed valid and enforceable to the
maximum extent possible.

                  (e) NOTICES. Any notice, demand or other communication
required, permitted or desired to be given hereunder shall be in writing and
shall be deemed effectively given upon personal delivery, facsimile transmission
(with confirmation of receipt), delivery by reputable overnight delivery service
(delivery, postage or freight charges prepaid) or on the fourth day following
deposit in the United States mail (if sent by certified or registered mail,
return receipt requested, delivery, postage or freight charges prepaid), in each
case duly addressed to the Company at its headquarters or to Employee at his
address of record listed with the Company.

                  (f) HEADINGS. The section headings herein are intended for
reference and shall not by themselves determine the construction or
interpretation of this Agreement.

                  (g) CONSTRUCTION. This Agreement shall be construed without
regard to any presumption or rule requiring construction against the party
causing such instrument or any portion thereof to be drafted. No rule of strict
construction will be applied for or against either of the parties hereto.



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                  (h) COUNTERPARTS. This Agreement may be executed in one or
more counterparts, each of which shall be an original but all of which shall
constitute one and the same instrument.

                  (i) EFFECT ON SUCCESSORS IN INTEREST. This Agreement shall be
binding upon the parties and upon their heirs, administrators, representatives,
executors and permitted assigns, and shall inure to the benefit of the parties
and each of them, and to their heirs, administrators, representatives, executors
and assigns.

                  (j) ARBITRATION. Any dispute regarding the application,
interpretation or breach of this Agreement or pertaining to Clements' employment
or termination of employment with the Company shall be resolved by final and
binding arbitration before the American Arbitration Association ("AAA") in
accordance with AAA's National Rules for the Resolution of Employment Disputes.
Attorney's fees and costs and may be awarded, in the discretion of the
Arbitrator, to the prevailing party in any dispute, and any resolution, opinion
or order of the Arbitrator may be entered as a judgment in a court of competent
jurisdiction.

                  (k) REVOCATION PERIOD. Clements shall have twenty-one (21)
days from receipt of this Agreement to consider this Agreement, and seven (7)
days following the signing of this Agreement to revoke it in writing, and this
Agreement shall not be effective or enforceable until the revocation period has
expired.

                  (l) ACKNOWLEDGMENT. Clements acknowledges that he fully
understands his right to discuss this Agreement with an attorney, that he has
carefully read and fully understands this entire Agreement and that he is
voluntarily entering into this Agreement.

         14. EXHIBITS. Attached hereto are true, complete and accurate copies of
the following documents concerning the 1997 Options and the Rollover Options:

                  (a) EXHIBIT A - Belden & Blake Corporation Stock Option Plan;

                  (b) EXHIBIT B - Form of Employee Stock Option Agreement used
for the Employee Stock Option Agreements dated May 28, 1994, August 24, 1995 and
August 26, 1996 and the Letter Agreement dated June 27, 1997 by and between the
Company and Clements amending the same; and

                  (c) EXHIBIT C - Nonqualified Stock Option Agreement dated June
27, 1997.



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         IN WITNESS WHEREOF, the parties hereto have executed and delivered this
Agreement effective as of the date set forth above.

                                            RONALD L. CLEMENTS

Dated:  May 24, 1999                        /s/ Ronald L. Clements
                                            -------------------------------
                                            Ronald L. Clements



                                            BELDEN & BLAKE CORPORATION,
                                            AN OHIO CORPORATION

Dated:  May 26, 1999                        By: /s/ Ronald E. Huff
                                               ----------------------------
                                            Title: President and CFO
                                                  -------------------------
                                            Name: Ronald E. Huff



                                            With respect to SECTION 8 only

                                            TPG PARTNERS II, L.P.

                                            By:      TPG GenPar II, L.P.
                                            By:      TPG Advisors II, Inc.

Dated:  May 24, 1999                        By: /s/ David M. Stanton
                                               ----------------------------
                                            Title: Vice-President
                                                  -------------------------




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