All persons holding administrative office at the time this Charter takes effect shall continue in office and in the performance of their duties until provision shall have been made in accordance therewith for the performance of such duties or the discontinuance of such office. The powers conferred and the duties imposed upon any office, department or agency of the City by the laws of the State shall, if such office, department or agency, be abolished by this Charter, or under its authority, be thereafter exercised and discharged by the office, department or agency designated by the Council unless otherwise provided herein.