The board shall, as soon as its members are elected and take office, provide for the performance of all the governmental functions of the county and to that end shall provide for and set up all necessary departments of government consistent with the provisions of this chapter. Any deputy county executive, assistant county executive, or department head may be removed at the pleasure of the board, except as the board may authorize the urban county executive to remove such employees, and such removal shall not be subject to review by any other county employee, agency, board or commission or under the grievance procedure adopted pursuant to § 15.2-1506. The board shall have all authority and powers provided for by this chapter or by other law and shall have the power to raise annually by taxes and assessments on property, persons and other subjects of taxation, which are not prohibited by law, such sums of money as in the judgment of the board are necessary to pay the debts, defray the expenses, accomplish the purposes and perform the functions of the county. However, any department head who could grieve his own removal from an office held prior to July 1, 1987, under the law in effect at the time he was appointed to office, shall retain such right to grieve his own removal from that office unless that right is waived in writing in consideration of a payment mutually agreed to by that department head and by the board.