The local board serving a single city shall be, at the discretion of the city council, either a local government official or a local board consisting of five members appointed by the city council of such city in accordance with the provisions of § 63.2-301. The city council may appoint one of its members to the local board. When a member of the city council who was appointed as a member of the local board ceases to be a member of the city council, his office as a member of the local board shall also be vacated and another member of the city council may be appointed to fill the vacancy. If a local government official constitutes the local board, he may designate a senior staff person in the local department to act in his behalf, in his absence, with respect to approving, cancelling or changing grants made under the provisions of this title.