Upon the establishment of a board of parks and recreation, the terms of the four members initially appointed by the mayor shall be one, two, three and four years respectively. Thereafter as a term expires, each new appointment shall be for a four-year term. All terms shall expire on the first Monday in January, but an appointee shall continue in office until his successor is appointed. If a vacancy on the board occurs, the mayor shall appoint a member for the unexpired term. (Prior code § 19-7)