Members of a board of an authority created under a statute or section of law repealed by this act with the same or similar name and functions shall continue in office for the duration of the terms of office for which they were appointed. Members shall be appointed under this act only as terms of the former members expire or vacancies occur. Members of the board of an authority created under a statute or section of law repealed by this act may be appointed to the new board to succeed themselves subject to any limits for the total period of service set forth in this act.