Beginning on January 9, 1989, the governor of the state of Missouri, by and with the advice and consent of the senate, shall appoint the four commissioners provided for in section 84.020, and one commissioner shall be appointed for a term of one year; one commissioner shall be appointed for a term of two years; one commissioner shall be appointed for a term of three years; one commissioner shall be appointed for a term of four years. Their successors shall each be appointed for a term of four years, and said commissioners shall hold office for their term of appointment and until their successors shall have been appointed and qualified. In case of a vacancy in said board for any cause whatsoever, it shall be filled by appointment for the unexpired term, in the same manner as in the case of original appointments. The governor shall issue commissions to the persons so appointed, designating the time for which they are appointed in case the appointment is to fill an unexpired term occasioned by death, resignation or any other cause, and whenever the term of office of any commissioner expires, the appointment of his successor shall be for four years. The commissioners now holding offices under existing laws in any city of this state to which sections 84.010 to 84.340 apply are to hold their offices until the expiration of their terms, and their successors are duly appointed and qualified.