<PAGE>

                                                                    EXHIBIT 4(k)

                               TENDER AGREEMENT

     This Tender Agreement ("Agreement") is entered into as of January 22, 2001,
by and between SYSCO Corporation, a Delaware corporation ("Parent"), and Teri E.
Unsworth ("Stockholder").

                                   RECITALS

     A. Parent, Sysco Food Services of New Jersey, Inc., a Delaware corporation
and a wholly owned subsidiary of Parent ("Merger Sub"), and Guest Supply, Inc.,
a New Jersey corporation (the "Company"), are entering into an Merger Agreement
and Plan of Reorganization of even date herewith (the "Merger Agreement") which
provides (subject to the conditions set forth therein) for the acquisition of
shares of Common Stock of the Company by Parent pursuant to a tender offer
followed by the merger of Merger Sub and the Company (the "Merger").

     B. In order to induce Parent and Merger Sub to enter into the Merger
Agreement, Stockholder is entering into this Agreement.

                                   AGREEMENT

     The parties to this Agreement, intending to be legally bound, agree as
follows:

                                   SECTION 1


                              CERTAIN DEFINITIONS


For purposes of this Agreement:

     (a) "Company Common Stock" shall mean the common stock, no par value per
share, of the Company.

     (b) "Expiration Date" shall mean the earliest of (i) the date upon which
the Merger Agreement is terminated; (ii) the date upon which the Merger is
effected; (iii) the date upon which all of the Stockholder's now owned or
hereafter acquired shares of Company Common Stock are purchased by Parent or
Merger Sub pursuant to the Offer (as defined in the Merger Agreement) and (iv)
the date on which the Offer terminates without the purchase of Company Common
Stock thereunder.

     (c) Stockholder shall be deemed to "Own" or to have acquired "Ownership" of
a security if Stockholder: (i) is the record owner of such security; or (ii) is
the "beneficial owner" (within the meaning of Rule 13d-3 under the Securities
Exchange Act of 1934) of such security.
<PAGE>

          (d) "Person" shall mean any (i) individual, (ii) corporation, limited
liability company, partnership or other entity, or (iii) governmental authority.

     (e) "Subject Securities" shall mean: (i) all securities of the Company
(including all shares of Company Common Stock and all options, warrants and
other rights to acquire shares of Company Common Stock) Owned by Stockholder as
of the date of this Agreement as set forth on the Schedule attached hereto; and
(ii) all additional securities of the Company (including all additional shares
of Company Common Stock and all additional options, warrants and other rights to
acquire shares of Company Common Stock) of which Stockholder acquires Ownership
during the period from the date of this Agreement through the Expiration Date.

     (f) A Person shall be deemed to have effected a "Transfer" of a security if
such Person directly or indirectly: (i) sells, pledges, encumbers, grants an
option with respect to, transfers or disposes of such security or any interest
in such security; or (ii) enters into an agreement or commitment contemplating
the possible sale of, pledge of, encumbrance of, grant of an option with respect
to, transfer of or disposition of such security or any interest therein.


                                  SECTION 2.

                               TENDER OF SHARES


     2.1      Tender Agreement.  Stockholder agrees, pursuant to the terms and
              ----------------
subject to the conditions set forth herein:

     (a) to tender for exchange in the Offer all shares of Company Common Stock
currently held by Stockholder as set forth on the signature page hereto and any
additional shares of Company Common Stock acquired by Stockholder (whether by
purchase, upon conversion of options or convertible securities, or otherwise)
after the date of this Agreement (collectively, the "Stockholder's Shares");

     (b) as promptly as practicable (but no later than ten (10) business days)
after commencement of the Offer (or, in the case of shares of Company Common
Stock acquired by Stockholder after commencement of the Offer, as promptly as
practicable after such acquisition) Stockholder shall, as appropriate, (x)
deliver to the Exchange Agent (the "Exchange Agent") designated in the Offer (i)
a letter of transmittal with respect to the Stockholder's Shares (other than the
Tender Exception Shares as defined in Section 2.3 below) complying with the
terms of the Offer together with instructions directing the Exchange Agent to
make payment for the Stockholder's Shares directly to Stockholder, (ii) a
certificate or certificates representing the Stockholder's Shares and (iii) all
other documents or instruments required to be delivered pursuant to the terms of
the Offer (collectively, the "Tender Documents"), and/or (y) instruct its broker
or such other Person who is the holder of record of any shares of Common Stock
Owned by Stockholder to tender such shares for exchange in the Offer pursuant to
the terms and conditions of the Offer; and
<PAGE>

     (c) Stockholder shall not withdraw any tender effected in accordance with
this Section 2.1; provided, however, that Stockholder shall have the right to
                  --------  -------
withdraw any tender effected in accordance with this Section 2.1 if the Merger
Agreement is terminated.

     2.2 Proxy. Stockholder hereby irrevocably (to the fullest extent permitted
         -----
by law) appoints and constitutes each of Merger Sub and Parent the attorneys and
proxies of the undersigned with full power of substitution and resubstitution,
to the full extent of the undersigned's rights with respect to the Subject
Securities. Upon the execution hereof, all prior proxies given by the
Stockholder with respect to any of the Shares are hereby revoked, and the
Stockholder agrees that no subsequent proxies will be given with respect to any
of the Subject Securities.

     This proxy is irrevocable, is coupled with an interest between Parent and
the Stockholder and is granted in consideration of Parent entering into the
Merger Agreement.

     The attorneys and proxies named above will be empowered, and may exercise
this proxy, to vote the Shares at any time until the Expiration Date at any
meeting of the stockholders of the Company, however called, or in connection
with any solicitation of written consents from stockholders of the Company, (i)
in favor of the approval and adoption of the Merger Agreement and the approval
of the Merger, and in favor of each of the other actions contemplated by the
Merger Agreement, (ii) against any proposal for any recapitalization, merger,
sale of assets or other business combination between the Company and any person
or entity (other than the Merger) and (iii) against any action or agreement that
would result in a breach of any covenant, representation or warranty contained
in the Merger Agreement or would result in any obligation or agreement of the
Company under the Merger Agreement not being fulfilled or would result in the
Company being required to pay to Parent or Merger Sub the fee contemplated in
Section 7.2 of the Merger Agreement.

     The Stockholder may vote the Subject Securities on all other matters. This
proxy shall be binding upon the heirs, estate, executors, personal
representatives, successors and assigns of the Stockholder (including any
transferee of any of the Subject Securities).

     This proxy shall terminate upon the Expiration Date.

     2.3 Limited Sales of Subject Securities.  Notwithstanding the provisions of
         -----------------------------------
Section 2.1 or 2.2 above, Parent and Merger Sub hereby agree that Stockholder
shall be entitled to sell, transfer and dispose of through sales in the public
markets, at any time up to five (5) days prior to the expiration of the Offer
(the "Tender Deadline"), a number of Stockholder's Shares that shall not exceed
fifteen percent (15%) of the aggregate numbers of shares of Company Common Stock
included in, or acquirable by Stockholder pursuant to, the Subject Securities
referred to in clause (i) of Section 1(e) (the "Tender Exception Shares"). Any
Tender Exception Shares not disposed of by the Stockholder by the Tender
Deadline shall be subject to the provisions of Sections 2.1 and 2.2 above.
<PAGE>

                                  SECTION 3.


                 REPRESENTATIONS AND WARRANTIES OF STOCKHOLDER

          Stockholder hereby represents and warrants to Parent as follows:

     3.1 Authorization, etc. Stockholder has the absolute and unrestricted
         ------------------
right, power, authority and capacity to execute and deliver this Agreement and
to perform his obligations hereunder and thereunder. This Agreement has been
duly executed and delivered by Stockholder and constitutes legal, valid and
binding obligations of Stockholder, enforceable against Stockholder in
accordance with their terms, subject to (i) laws of general application relating
to bankruptcy, insolvency and the relief of debtors, and (ii) rules of law
governing specific performance, injunctive relief and other equitable remedies.

     3.2 No Conflicts or Consents.
         ------------------------

     (a) The execution and delivery of this Agreement by Stockholder do not,
and, to the Stockholder's knowledge as of the date of this Agreement, the
performance of this Agreement by Stockholder in accordance with its terms will
not: (i) conflict with or violate any law, rule, regulation, order, decree or
judgment applicable to Stockholder or by which he or any of his properties is or
may be bound or affected; or (ii) result in or constitute (with or without
notice or lapse of time) any breach of or default under, or give to any other
Person (with or without notice or lapse of time) any right of termination,
amendment, acceleration or cancellation of, or result (with or without notice or
lapse of time) in the creation of any encumbrance or restriction on any of the
Subject Securities pursuant to, any contract to which Stockholder is a party or
by which Stockholder or any of his affiliates or properties is or may be bound
or affected.

     (b) The execution and delivery of this Agreement by Stockholder do not, and
the performance of this Agreement by Stockholder will not, require any consent
or approval of any Person.

     3.3 Title to Securities. As of the date of this Agreement: (a) Stockholder
         -------------------
holds of record (free and clear of any encumbrances or restrictions) the number
of outstanding shares of Company Common Stock set forth under the heading
"Shares Held of Record" on the Schedule attached hereto; (b) Stockholder holds
(free and clear of any encumbrances or restrictions) the options, warrants and
other rights to acquire shares of Company Common Stock set forth under the
heading "Options and Other Rights" on the Schedule attached hereto; (c)
Stockholder Owns the additional securities of the Company set forth under the
heading "Additional Securities Beneficially Owned" on the Schedule attached
hereto; and (d) Stockholder does not directly or indirectly Own any shares of
capital stock or other securities of the Company, or any option, warrant or
other right to acquire (by purchase, conversion or otherwise) any shares of
capital stock or other securities of the Company, other than the shares and
options, warrants and other rights set forth on the on the Schedule attached
hereto.

     3.4 Accuracy of Representations.  The representations and warranties
         ---------------------------
contained in
<PAGE>

this Agreement are accurate in all respects as of the date of this Agreement,
will be accurate in all respects at all times through the Expiration Date and
will be accurate in all respects as of the date of the consummation of the
Merger as if made on that date.

     3.5 Finder's Fees. No investment banker, broker, finder or other Person is
         -------------
entitled to a commission or fee from Parent or Merger Sub in respect of this
Agreement based upon any arrangement or agreement made by or on behalf of
Stockholder other than any arrangement or agreement made by or on behalf of the
Company.

                                  SECTION 4.


                      ADDITIONAL COVENANTS OF STOCKHOLDER

     4.1 Further Assurances. Stockholder agrees that, subject to the fiduciary
         -----------------
duty under applicable law of Stockholder as a director of the Company (if
Stockholder is such a director) as further provided in the Merger Agreement, it
shall not take any action which in any manner delays, deters or impedes the
successful completion of the Offer and the Merger in an expeditious manner. In
addition, from time to time and without additional consideration, Stockholder
shall execute and deliver, or cause to be executed and delivered, such
additional transfers, assignments, endorsements, proxies, consents and other
instruments, and shall take such further actions, as Parent may reasonably
request for the purpose of carrying out and furthering the intent of this
Agreement.

     4.2 No Proxies for or Encumbrances on Subject Securities. Except pursuant
         ----------------------------------------------------
to the terms of this Agreement or the Tender Documents, Stockholder shall not,
without the prior written consent of Parent, directly or indirectly, (i) grant
any proxies or enter into any voting trust or other agreement or arrangement
with respect to the voting of any Subject Securities or (ii) sell, assign,
transfer, encumber or otherwise dispose of, or enter into any contract, option
or other arrangement or understanding with respect to the direct or indirect
sale, assignment, transfer, encumbrance or other disposition of, any Subject
Securities during the term of this Agreement.

     4.3 No Shopping. Stockholder, in the capacity as a stockholder, shall not
         -----------
directly or indirectly, subject to the fiduciary duty under applicable law of
Stockholder as a director of the Company (if Stockholder is such a director),
take any action prohibited by Section 3.5 of the Merger Agreement.

     4.4 Conduct of Stockholder. Stockholder will not (i) take, agree or commit
         ----------------------
to take any action that would make any representation and warranty of
Stockholder hereunder inaccurate in any respect as of any time prior to the
termination of this Agreement or (ii) omit, or agree or commit to omit, to take
any reasonable action necessary to prevent any such representation or warranty
from being inaccurate in any respect at any such time.

     4.5 Disclosure. Stockholder hereby permits Parent to publish and disclose
         ----------
in the offer documents and, if approval of the Company's stockholders is
required under applicable law, a
<PAGE>

proxy statement (including all documents and schedules to be filed in connection
therewith with the SEC) such Stockholder's identity and details regarding his
ownership of shares of Company Common Stock and the nature of his commitments,
arrangements and understandings under this Agreement.

     4.6  Action by the Board of Directors of the Company. Stockholder agrees
          -----------------------------------------------
that, subject to the fiduciary duty under applicable law of Stockholder as a
director of the Company (if Stockholder is such a director), he shall take such
actions at the first meeting of the Board of Directors of the Company following
the Effective Time (as defined in the Merger Agreement) as shall be necessary to
permit the Company to comply with its obligations under Section 1.4 of the
Merger Agreement including, without limitation, voting to increase the size of
the Board of Directors of the Company, voting to elect as directors of the
Company those individuals designated by Sysco and/or resigning as a director of
the Company.

                                  SECTION 5.

                                 MISCELLANEOUS

     5.1  Expenses.  All costs and expenses incurred in connection with the
          --------
transactions contemplated by this Agreement shall be paid by the party incurring
such costs and expenses.

     5.2  Notices. Any notice or other communication required or permitted to be
          -------
delivered to either party under this Agreement shall be in writing and shall be
deemed properly delivered, given and received when delivered (by hand, by
registered mail, by courier or express delivery service or by facsimile) to the
address or facsimile telephone number set forth beneath the name of such party
below (or to such other address or facsimile telephone number as such party
shall have specified in a written notice given to the other party): if to
Stockholder: at the address set forth below Stockholder's signature on the
signature page hereof if to Parent: SYSCO Corporation, 1390 Enclave Parkway,
Houston, TX 77077-2099, Attn: General Counsel

     5.3  Severability. If any provision of this Agreement or any part of any
          ------------
such provision is held under any circumstances to be invalid or unenforceable in
any jurisdiction, then (a) such provision or part thereof shall, with respect to
such circumstances and in such jurisdiction, be deemed amended to conform to
applicable laws so as to be valid and enforceable to the fullest possible
extent, (b) the invalidity or unenforceability of such provision or part thereof
under such circumstances and in such jurisdiction shall not affect the validity
or enforceability of such provision or part thereof under any other
circumstances or in any other jurisdiction, and (c) the invalidity or
unenforceability of such provision or part thereof shall not affect the validity
or enforceability of the remainder of such provision or the validity or
enforceability of any other provision of this Agreement. Each provision of this
Agreement is separable from every other provision of this Agreement, and each
part of each provision of this Agreement is separable from every other part of
such provision.

     5.4  Entire Agreement. This Agreement, the Proxy and any other documents
          ----------------
delivered by the parties in connection herewith constitute the entire agreement
between the parties with respect to the subject matter hereof and thereof and
supersede all prior agreements and
<PAGE>

understandings between the parties with respect thereto. No addition to or
modification of any provision of this Agreement shall be binding upon either
party unless made in writing and signed by both parties.

     5.5 Assignment; Binding Effect. Except as provided herein, neither this
         --------------------------
Agreement nor any of the interests or obligations hereunder may be assigned or
delegated by Stockholder, and any attempted or purported assignment or
delegation of any of such interests or obligations shall be void. Subject to the
preceding sentence, this Agreement shall be binding upon Stockholder and his
heirs, estate, executors, personal representatives, successors and assigns, and
shall inure to the benefit of Parent and its successors and assigns. Without
limiting any of the restrictions set forth in this Agreement, this Agreement
shall be binding upon any Person to whom any Subject Securities are transferred
other than with respect to Subject Securities transferred pursuant to Section
2.3. Nothing in this Agreement is intended to confer on any Person (other than
Parent and its successors and assigns) any rights or remedies of any nature.

     5.6 Specific Performance. The parties agree that irreparable damage would
         --------------------
occur in the event that any of the provisions of this Agreement or the Proxy was
not performed in accordance with its specific terms or was otherwise breached.
Stockholder agrees that, in the event of any breach or threatened breach by
Stockholder of any covenant or obligation contained in this Agreement or in the
Proxy, Parent shall be entitled (in addition to any other remedy that may be
available to it, including monetary damages) to seek and obtain (a) a decree or
order of specific performance to enforce the observance and performance of such
covenant or obligation, and (b) an injunction restraining such breach or
threatened breach. Stockholder further agrees that neither Parent nor any other
Person shall be required to obtain, furnish or post any bond or similar
instrument in connection with or as a condition to obtaining any remedy referred
to in this Section 5.6, and Stockholder irrevocably waives any right he may have
to require the obtaining, furnishing or posting of any such bond or similar
instrument.

     5.7 Non-Exclusivity. The rights and remedies of Parent under this Agreement
         ---------------
are not exclusive of or limited by any other rights or remedies which it may
have, whether at law, in equity, by contract or otherwise, all of which shall be
cumulative (and not alternative). Without limiting the generality of the
foregoing, the rights and remedies of Parent under this Agreement, and the
obligations and liabilities of Stockholder under this Agreement, are in addition
to their respective rights, remedies, obligations and liabilities under common
law requirements and under all applicable statutes, rules and regulations.
Nothing in this Agreement shall limit any of Stockholder's obligations, or the
rights or remedies of Parent, under any Affiliate Agreement between Parent and
Stockholder; and nothing in any such Affiliate Agreement shall limit any of
Stockholder's obligations, or any of the rights or remedies of Parent, under
this Agreement.

     5.8 Governing Law; Venue.
         --------------------

     (a) This Agreement shall be construed in accordance with, and governed in
all respects by, the laws of the State of Delaware (without giving effect to
principles of conflicts of laws).

     (b) Any legal action or other legal proceeding relating to this Agreement
or the Proxy or the enforcement of any provision of this Agreement or the Proxy
shall be brought or otherwise
<PAGE>

commenced in any state or federal court located in the State of Delaware. Each
of Stockholder and Parent:

     (i)   expressly and irrevocably consents and submits to the jurisdiction of
each state and federal court located in the State of Delaware in connection with
any such legal proceeding;

     (ii)  agrees that service of any process, summons, notice or document by
U.S. mail addressed to him at the address set forth below shall constitute
effective service of such process, summons, notice or document for purposes of
any such legal proceeding;

     (iii) agrees that each state and federal court located in the State of
Delaware shall be deemed to be a convenient forum; and

     (iv)  agrees not to assert (by way of motion, as a defense or otherwise),
in any such legal proceeding commenced in any state or federal court located in
the State of Delaware, any claim that Stockholder is not subject personally to
the jurisdiction of such court, that such legal proceeding has been brought in
an inconvenient forum, that the venue of such proceeding is improper or that
this Agreement or the subject matter of this Agreement may not be enforced in or
by such court.

     (c) EACH OF STOCKHOLDER AND PARENT IRREVOCABLY WAIVES THE RIGHT TO A JURY
TRIAL IN CONNECTION WITH ANY LEGAL PROCEEDING RELATING TO THIS AGREEMENT OR THE
PROXY OR THE ENFORCEMENT OF ANY PROVISION OF THIS AGREEMENT OR THE PROXY.

     5.9  Counterparts. This Agreement may be executed by the parties in
          ------------
separate counterparts, each of which when so executed and delivered shall be an
original, but all such counterparts shall together constitute one and the same
instrument.

     5.10 Captions. The captions contained in this Agreement are for convenience
          --------
of reference only, shall not be deemed to be a part of this Agreement and shall
not be referred to in connection with the construction or interpretation of this
Agreement.

     5.11 Attorneys' Fees. If any legal action or other legal proceeding
          ---------------
relating to this Agreement or the enforcement of any provision of this Agreement
is brought against Stockholder, the prevailing party shall be entitled to
recover reasonable attorneys' fees, costs and disbursements (in addition to any
other relief to which the prevailing party may be entitled).

     5.12 Waiver. No failure on the part of Parent to exercise any power, right,
          ------
privilege or remedy under this Agreement, and no delay on the part of Parent in
exercising any power, right, privilege or remedy under this Agreement, shall
operate as a waiver of such power, right, privilege or remedy; and no single or
partial exercise of any such power, right, privilege or remedy shall preclude
any other or further exercise thereof or of any other power, right, privilege or
remedy. Parent shall not be deemed to have waived any claim available to Parent
arising out of this Agreement, or any power, right, privilege or remedy of
Parent under this Agreement, unless the waiver of such claim, power, right,
privilege or remedy is expressly set forth in a
<PAGE>

written instrument duly executed and delivered on behalf of Parent; and any such
waiver shall not be applicable or have any effect except in the specific
instance in which it is given.

     5.13 Termination. This Agreement will terminate immediately upon the
          -----------
Expiration Date.

     5.14 Construction.
          ------------

     (a)  For purposes of this Agreement, whenever the context requires: the
singular number shall include the plural, and vice versa; the masculine gender
shall include the feminine and neuter genders; the feminine gender shall include
the masculine and neuter genders; and the neuter gender shall include masculine
and feminine genders.

     (b)  The parties agree that any rule of construction to the effect that
ambiguities are to be resolved against the drafting party shall not be applied
in the construction or interpretation of this Agreement.

     (c)  As used in this Agreement, the words "include" and "including," and
variations thereof, shall not be deemed to be terms of limitation, but rather
shall be deemed to be followed by the words "without limitation."

     (d)  Except as otherwise indicated, all references in this Agreement to
"Sections" and "Exhibits" are intended to refer to Sections of this Agreement
and Exhibits to this Agreement.
<PAGE>

                 [REMAINDER OF PAGE INTENTIONALLY LEFT BLANK]


     In Witness Whereof, Parent and Stockholder have caused this Tender
Agreement to be executed as of the date first written above.

SYSCO CORPORATION

By: /s/ Michael C. Nichols
    --------------------------------------
        Michael C. Nichols, Vice President

Stockholder

By: /s/ Teri E. Unsworth
     -------------------------------------

Address:  1999 Oak Knoll Ave.
          San Marino, CA 91108
<PAGE>

                                   SCHEDULE
                                   --------



        NUMBER OF SHARES OF GUEST               NUMBER OF SHARES OF
     SUPPLY COMMON STOCK BENEFICIALLY              GUEST SUPPLY COMMON
     OWNED BUT NOT HELD OF RECORD               STOCK HELD OF RECORD
     ----------------------------               --------------------

               80,500                                  147,055