All persons holding office at the time this Charter is adopted, shall continue in office and in the performance of their duties until provision shall have been otherwise made in accordance with this Charter for the performance or discontinuance of the duties of any such office. When such provision shall have been made the term of any such officer shall expire and the office be deemed abolished. The powers which are conferred and the duties which are imposed upon any officer, board or department of the city under the laws of the state, or under any city ordinance or contract in force at the time of the taking effect of this act shall, if such office or department is abolished by this Charter, be thereafter exercised and discharged by the commission, officer, board or department upon whom are imposed corresponding functions, powers and duties by this Charter or by any ordinance or resolution of the city thereafter enacted.