Whenever the owner of a registered and licensed vehicle transfers his ownership therein, he shall immediately notify the Department of Motor Vehicles in writing, giving the name and address of the new owner and the date of transfer. The license plate issued for the vehicle shall remain with the prior owner who, within thirty days of the transfer, either shall apply for the transfer of the plate pursuant to § 56-3-1290 or shall return the plate to the Department; in either event the registration card shall be concurrently returned to the Department. If the vehicle is registered and licensed in the name of the State, any department, agency, or political subdivision of the State, or any department or agency of such a subdivision and a reduced registration and license fee has been paid, the owner shall return the registration card and the plate issued for the vehicle to the Department for cancellation, unless the transfer is made to another like agency qualified to obtain a registration and license of the vehicle at the reduced rate.