(A)   The Mayor shall have the power to appoint, by and with the advice and consent of the City Council, all officers of the city except the City Clerk.
   (B)   Whenever a vacancy shall occur in any office which, by law or ordinance, the Mayor is empowered and required to fill, the Mayor shall, at the first regular meeting after the vacancy occurred, designate a suitable person to discharge the functions of the office.
('74 Code, § 2-44)