The elective offices of City Clerk and City Treasurer are hereby replaced by the appointed offices of City Clerk and City Treasurer in accordance with this Charter. Those persons, at the time of the initial adoption of this Charter, shall continue in the appointed position of City Clerk and City Treasurer for a period of one hundred and twenty (120) days after the 1993 general election; at which time these positions shall be appointed in accordance with this Charter. Nothing herein shall prevent those persons currently holding the positions of City Clerk and City Treasurer from being appointed to those positions.