<PAGE>

                                                                     EXHIBIT 4.1


                             FIRST AMENDMENT TO THE

                  AMENDED AND RESTATED NOTE PURCHASE AGREEMENT

          THIS FIRST AMENDMENT TO THE AMENDED AND RESTATED NOTE PURCHASE
AGREEMENT, dated as of April 4, 2001 (this "Amendment") relates to that certain
                                            ---------
Amended and Restated Note Purchase Agreement dated as of October 29, 1999 (as
the same may be amended, supplemented, restated or otherwise modified from time
to time, the "Note Purchase Agreement") and is entered into between TeleCorp
              -----------------------
Wireless, Inc. (f/k/a TeleCorp PCS, Inc.) (the "Company") and Lucent
                                                -------
Technologies Inc. ("Lucent").  Capitalized terms used and not otherwise defined
                    ------
herein shall have the meanings assigned to them in the Note Purchase Agreement.

                              W I T N E S S E T H

          WHEREAS, the Company and Lucent have entered into the Note Purchase
Agreement;

          WHEREAS, the Company has requested that Lucent amend the Note Purchase
Agreement pursuant to a request dated April 3, 2001;

          WHEREAS, Lucent is willing to enter into such amendments on the terms
and conditions set forth herein;

          NOW, THEREFORE, in consideration of the above premises, the Company
and Lucent agree as follows:

  1.  Amendments to the Note Purchase Agreement.  Upon the "Effective Date" (as
      -----------------------------------------
defined in Section 3 below), the Note Purchase Agreement is hereby amended as
           ---------
follows:

      a.  Amendment to Section 6.8(a) of the Disclosure Schedule.
          ------------------------------------------------------

          Section 6.8(a) of the Disclosure Schedule (referred to in Section
      6.8(a)) is hereby deleted and substituted therefor is the following:

          "The authorized Capital Stock of the Company consists of 3,000 shares
          of Common Stock, par value $.01 per share, of which 1,000 shares are
          outstanding. All outstanding shares of Common Stock of the Company are
          held by TeleCorp PCS, Inc."

      b.  Amendment to Section 6.21(e).
          ----------------------------

          Subsection (e) of Section 6.21(e) is hereby amended by deleting the
      first sentence thereof in its entirety.

      c.  Amendment to Section 10.4. Section 10.4 of the Note Purchase
          -------------------------
  Agreement is hereby amended by deleting the amount "$198,000,000" from each
place where it appears and substituting therefor the amount "$368,141,400".
<PAGE>

      d.  Amendments to Section 11.4.
          --------------------------

          Section 11.4 is hereby deleted in its entirety and substituted
      therefor is the following:

          "Unless (a) no Event of Default or Potential Event of Default shall
          exist which is continuing and (b) the Company shall have paid, in
          cash, all interest on the Notes on each of the prior three Payment
          Dates, the Company shall not declare or make any Restricted Payment;
          provided that the restriction set forth in clause (b) shall not apply
          --------
          to Restricted Payments made by the Company to TeleCorp PCS, Inc. in
          respect of (i) the repurchase or redemption of any Capital Stock of
          TeleCorp PCS, Inc. held by any member of management of TeleCorp PCS,
          Inc. or any Subsidiary thereof pursuant to a management subscription
          agreement, stock option agreement, restricted stock option agreement,
          put agreement or other similar agreement in an amount not to exceed
          $10,000,000 in any twelve-month period (it being understood that any
          portion which is not used in any twelve-month period may be carried
          forward to one or more future twelve-month periods so long as the
          aggregate of all unused amounts that may be carried forward to any
          twelve-month period shall not exceed $20,000,000) and (ii) any purpose
          of TeleCorp PCS, Inc. in an amount not to exceed $10,000,000 in any
          fiscal year).

          To the extent that proceeds of the sale of TeleCorp PCS, Inc.'s Parent
          Notes are contributed by TeleCorp PCS, Inc. as a capital contribution
          to the Company, the Company may make Restricted Payments to TeleCorp
          PCS, Inc. or any of its subsidiaries (as directed by TeleCorp PCS,
          Inc.) in cash, and without restriction, in an amount equal to such
          equity proceeds, such amount not to exceed the amount of Excess Cash
          Flow (as defined in the Credit Agreement) generated after the date
          such equity investment first occurs or, if greater, an amount not in
          excess of Excess Cash Flow (as defined in the Credit Agreement) for
          the fiscal year most recently ended."

      e.  Amendments to Section 15.
          ------------------------

          i. The definition of "Company" in Section 15 is hereby deleted in its
      entirety and substituted therefor is the following:

          "Company:  TeleCorp Wireless, Inc."
           -------

          ii. The definition of "Credit Agreement" in Section 15 is hereby
      deleted in its entirety and substituted therefor is the following:

          "Credit Agreement:  Amended and Restated Credit Agreement dated
           ----------------
          as of October 2, 2000 among the Company, the Lenders, the
          Administrative Agent, TD Securities (USA) Inc. as Syndication Agent
          and Bankers Trust Company, as Documentation Agent."

                                       2
<PAGE>

          iii. The definition of "Management Agreement" in Section 15 is hereby
      deleted in its entirety and substituted therefor is the following:

          "Management Agreement:  the Management Agreement between TeleCorp
           --------------------
          PCS, Inc. and TeleCorp Management Corp. dated as of July 17, 1998 as
          amended by Amendment No. 1 thereto dated as of May 25, 1999, as the
          same may be amended from time to time."

          iv. The definition of "POPs" in Section 15 is hereby deleted in its
      entirety and substituted therefor is the following:

          "POPs:  as of any date, with respect to any BTA or MTA, the
           ----
          population of such BTA or MTA as such number is published in the then
          most recently issued retail marketing reports by Kagan Guide."

          v.  The definition of "Series A Note Commitment" in Section 15 is
      hereby deleted in its entirety and substituted therefor is the following:

          "Series A Note Commitment:  your commitment to purchase
           ------------------------
          $40,000,000 in aggregate principal amount of Series A Notes that
          have previously been issued, and to purchase additional Series A
          Notes in an aggregate principal amount equal to $37,500,000 pursuant
          to Section 1 and Section 28 which amount shall be decreased on a
          dollar for dollar basis to the extent the Company receives Net
          Securities Proceeds from Equity Issuances in an aggregate principal
          amount which exceeds $368,141,400."

          vi. The definition of "Series A Note Commitment Termination Date" in
      Section 15 is hereby deleted in its entirety and substituted therefor is
      the following:

          "Series A Note Commitment Termination Date:  The earlier to occur
           -----------------------------------------
          of (a) October 31, 2001 or (b) such earlier date on which the Series A
          Note Commitment shall terminate pursuant to the terms of the
          Agreement."

          vii. The definition of "Series B Availability Period" in Section 15 is
      hereby deleted in its entirety and substituted therefor is the following:

          "Series B Availability Period:  the period commencing on October
           ----------------------------
          29, 1999 and continuing to but excluding October 31, 2002."

          viii. The definition of "Series B Note Commitment" in Section 15 is
      hereby deleted in its entirety and substituted therefor is the following:

          "Series B Note Commitment:  your commitment to purchase Series B
           ------------------------
          Notes in an aggregate principal amount equal to $37,500,000."

                                       3
<PAGE>

          ix. The definition of "Series B Note Commitment Termination Date" in
      Section 15 is hereby deleted in its entirety and substituted therefor is
      the following:

          "Series B Note Commitment Termination Date:  October 31, 2002 or
           -----------------------------------------
          such earlier date on which the Series B Note Commitment shall
          terminate pursuant to the terms of this Agreement."

          x. The definition of "Stockholders' Agreement" in Section 15 is hereby
      deleted in its entirety and substituted therefor is the following:

          "Stockholders' Agreement:  the Stockholders' Agreement dated as
           -----------------------
          of November 13, 2000, among AT&T PCS, TWR, the Cash Equity Investors,
          the Management Stockholders and TeleCorp PCS, Inc., as such agreement
          may be amended from time to time in accordance with the provisions of
          such agreement, so long as the terms of any such amendment are no less
          favorable to the holders of the Notes than the terms of the
          Stockholders' Agreement in effect on the date of the Indenture."

          xi. The definition of "TeleCorp Holdings" in Section 15 is hereby
      deleted in its entirety and substituted therefor is the following:

          "TeleCorp Holdings:  TeleCorp Holding Corp., LLC, a Delaware
           -----------------
          limited liability company."

          xii. The following definition of "Parent Notes" in Section 15 is
      hereby added:

          "Parent Notes: TeleCorp PCS, Inc. Senior Subordinated Discount
           ------------
          Notes due 2011."

      f.  Amendment to Section 28.
          -----------------------

          i. Section 28 is hereby amended by inserting in the first paragraph
      thereof, immediately after the phrase "provided that" and before the
                                             --------
      number "(i)", the following clause:

          "after the Series A Note Commitment Termination Date all of the Notes
          purchased by you shall have the same terms as the Series B Notes; and
          provided further that"
          -------- -------

          ii. Section 28 is hereby amended by deleting therefrom the paragraph
      that reads "Your exclusivity rights under the Procurement Contract with
      respect to the Expansion Area shall not terminate if any of these
      conditions are not satisfied and as a result you do not purchase any
      Expansion Notes. The Company's and your obligations under this section 28
      shall expire June 30, 2001" in its entirety and substituting therefor the
      following:

                                       4
<PAGE>

               "Your exclusivity rights under the Procurement Contract with
               respect to the Expansion Area shall not terminate if any of these
               conditions are not satisfied and as a result you do not purchase
               any Expansion Notes.  The Company's and your obligations under
               this section 28 shall expire October 31, 2001 (with respect to
               the Series A Notes) and October 31, 2002 (with respect to the
               Series B Notes); provided that the Company may at any time
               terminate the Commitments in whole but not in part; provided
               further that if TeleCorp PCS, Inc. shall issue Parent Notes to
               Lucent and the aggregate amount of gross proceeds received by
               TeleCorp PCS, Inc. from the issuance of Parent Notes shall exceed
               $350,000,000, then the aggregate amount of the Commitments will
               be automatically reduced by the amount of such excess proceeds
               (such reduction to apply equally to the then outstanding Series A
               Note Commitment, if any, and the Series B Note Commitment; if the
               Series A Note Commitment shall have expired without having been
               fully drawn, then the Series B Note Commitment will be reduced by
               an amount equal to the excess of (i) the aggregate amount of
               gross proceeds received by TeleCorp PCS, Inc. from the issuance
               of Parent Notes over (ii) the sum of $350,000,000 plus the amount
               of the Series A Note Commitment that expired without having been
               drawn); and provided further that Lucent may elect, in respect of
               any request by the Company that Lucent purchase Expansion Notes,
               to instead purchase Parent Notes from TeleCorp PCS, Inc. in an
               amount that yields the same amount of gross proceeds to TeleCorp
               PCS, Inc. as the Company would have received from the issuance of
               the requested Expansion Notes."

               iii.  Section 28 of Note Purchase Agreement is hereby amended by
               deleting the following provision:


               "(i) modify the threshold amount of Net Securities Proceeds under
               section 10.4 to an amount not to exceed the product of (X)
               $198,000,000 multiplied by (Y) a fraction the numerator of which
               is the sum of (A) 16,800,000 plus (B) the number of POPs in
               Expansion Areas for which Expansion Notes have been or concurrent
               therewith are being issued and the denominator of which is
               16,800,000; and


               (ii)"

        2.  Representations and Warranties.  The Company hereby represents and
            ------------------------------
warrants to Lucent that, as of the Effective Date and after giving effect to
this Amendment:

            a. All the representations and warranties of the Company contained
        in this Amendment and the Note Purchase Agreement that are not qualified
        by Material Adverse Effect are true and correct in all material respects
        on and as of the Effective Date, as if then made (other than
        representations and warranties which expressly speak as of a different
        date, which shall be true and correct in all material respects as of
        that

                                       5
<PAGE>

        date, and other than the representation and warranty set forth in
        the first sentence of Section 6.8(a), which is true and correct as of
        the date of this Amendment), and all the representations and warranties
        of the Company contained in this Amendment and the Note Purchase
        Agreement that are qualified by Material Adverse Effect are true and
        correct on and as of the Effective Date, as if then made (other than
        representations and warranties which expressly speak as of a different
        date, which shall be true and correct as of that date); and

            b. No Event of Default or Potential Event of Default has occurred
        and is continuing or will result after giving effect to this Amendment.

        3.  Effective Date.  This Amendment shall become effective as of the
            --------------
date first written above (the "Effective Date") upon the satisfaction of each of
                               --------------
the following conditions:

            a. The Company shall have received each of the following documents,
        in each case in form and substance satisfactory to the Company, prior to
        5:00 p.m. (New York time) on April 6, 2001:

               i.  counterparts hereof executed by Lucent; and

               ii. such additional documentation as the Company may reasonably
            request.

            b. Lucent shall have received each of the following documents, in
        each case in form and substance satisfactory to Lucent, prior to 5:00
        p.m. (New York time) on April 6, 2001;

               i.  counterparts hereof executed by the Company;

               ii. a certificate of the Secretary or Assistant Secretary of the
            Company dated the Effective Date certifying (A) that the bylaws of
            the Company have not been amended or otherwise modified since the
            date of the most recent certification thereof by the Secretary or
            Assistant Secretary of the Company delivered to Lucent and remain in
            full force and effect as of the Effective Date, (B) that the charter
            of the Company has not been amended or otherwise modified since the
            date of the most recent certification thereof by the Secretary of
            State of the Company's jurisdiction of incorporation delivered to
            Lucent and remain in full force and effect as of the Effective Date
            and (C) that the execution, delivery and performance of this
            Amendment have been duly authorized by all necessary or proper
            corporate and shareholder action;

               iii. an opinion from counsel to the Company stating that the
            Amendment constitutes the legal, valid and binding obligation of the
            Company, enforceable against the Company in accordance with its
            terms; and

               iv. such additional documentation as Lucent may reasonably
            request.


                                       6
<PAGE>

            c. There shall be no suit, action, investigation, inquiry or other
        proceeding by or before any Governmental Authority or any other Person
        or any other legal or administrative proceeding, pending or, to the
        Company's knowledge, threatened, which questions the validity or
        legality of this Amendment or performance by the Company of its
        obligations under the Note Purchase Agreement and seeks damages or
        injunctive or other equitable relief in connection therewith;

            d. All the representations and warranties of the Company contained
        in this Amendment and the Note Purchase Agreement that are not qualified
        by Material Adverse Effect shall be true and correct in all material
        respects on and as of the Effective Date, as if then made (other than
        representations and warranties which expressly speak as of a different
        date, which shall be true and correct in all material respects as of
        that date), and all the representations and warranties of the Company
        contained in this Amendment and the Note Purchase Agreement that are
        qualified by Material Adverse Effect shall be true and correct on and as
        of the Effective Date, as if then made (other than representations and
        warranties which expressly speak as of a different date, which shall be
        true and correct as of that date);

            e. All corporate and other proceedings, and all documents,
        instruments and other legal matters in connection with the transactions
        contemplated by this Amendment shall be satisfactory in all respects in
        form and substance to Lucent and Lucent shall have received any other
        documents, instruments and legal opinions in respect of any aspect or
        consequence of this Amendment as it may reasonably request; and

            f. No Event of Default or Potential Event of Default shall have
        occurred and be continuing or will result after giving effect to this
        Amendment.

        4.  Reference to and Effect on the Note Purchase Agreement.
            ------------------------------------------------------

            a. Upon the Effective Date, each reference in the Note Purchase
        Agreement to "this Agreement", "hereunder", "hereof" or words of like
        import shall mean and be a reference to the Note Purchase Agreement as
        amended and supplemented hereby.

            b. Except to the extent specifically set forth herein, the
        provisions of the Note Purchase Agreement shall not be amended,
        modified, waived, impaired or otherwise affected hereby, and such Note
        Purchase Agreement and the obligations thereunder are hereby confirmed
        as being in full force and effect.

            c. This Amendment shall be limited solely to the matters expressly
        set forth herein and shall not (i) constitute an amendment or waiver of
        any other term or condition of the Note Purchase Agreement, (ii)
        prejudice any right or rights which Lucent or any Holder may now have or
        may have in the future under or in connection with the Note Purchase
        Agreement, (iii) require Lucent or any Holder to agree to a similar
        transaction on a future occasion or (iv) create any right herein to
        another Person or other beneficiary or otherwise, except to the extent
        specifically provided herein.

                                       7
<PAGE>

        5.  Headings.  The headings herein are for convenience of reference
            --------
only and shall not alter or otherwise affect the meaning hereof.

        6.  Section Titles.  The Section titles in this Amendment are and
            --------------
shall be without substantive meaning or content of any kind whatsoever and are
not a part of the agreement between the parties hereto.

        7.  Counterparts.  This Amendment may be executed by one or more of
            ------------
the parties to this Amendment on any number of separate counterparts (including
by telecopy), and all said counterparts taken together shall be deemed to
constitute one and the same instrument. A set of the copies of this Amendment
signed by all the parties shall be lodged with the Company and Lucent.

        8.  GOVERNING LAW.  THIS AMENDMENT, AND ALL MATTERS OF CONSTRUCTION,
            -------------
VALIDITY AND PERFORMANCE HEREOF, SHALL BE GOVERNED BY, AND CONSTRUED AND
INTERPRETED IN ACCORDANCE WITH, THE LAW OF THE STATE OF NEW YORK WITHOUT REGARD
TO THE PRINCIPLES OF CONFLICT OF LAWS THEREOF OTHER THAN SECTION 5-1401 OF THE
GENERAL OBLIGATIONS LAW OF THE STATE OF NEW YORK.

        9.  No Strict Construction.  The parties hereto have participated
            ----------------------
jointly in the negotiation and drafting of this Amendment. In the event an
ambiguity or question of intent or interpretation arises, this Amendment shall
be construed as if drafted jointly by the parties hereto and no presumption or
burden of proof shall arise favoring or disfavoring any party by virtue of the
authorship of any provisions of this Amendment.

                                       8
<PAGE>

          IN WITNESS WHEREOF, the Company and Lucent have caused this Amendment
to be duly executed and delivered by their proper and duly authorized officers
as of the day and year first above written.

                                         TELECORP WIRELESS, INC.



                                         By:  /s/ Thomas H. Sullivan
                                             -------------------------
                                              Name:  Thomas H. Sullivan
                                              Title: President


                                         LUCENT TECHNOLOGIES INC.



                                         By:  /s/ Robert Grant
                                             -------------------------
                                              Name:  Robert Grant
                                              Title: Director




                                Signature Page