Wherever by virtue of Statute or charter provisions appointive offices of any municipality are placed under the terms and provisions of Civil Service and rules are set up governing appointment to and removal from such offices, the provisions of Article 16, § 30, of the Texas Constitution limiting the duration of all offices not fixed by the Constitution to two (2) years shall not apply, but the duration of such offices shall be governed by the provisions of the Civil Service law or charter provisions applicable thereto.