Mo. Rev. Stat. § 172.050
The governor shall, by and with the advice and consent of the senate, fill all vacancies caused by the expiration of the term of office of any curator, and he shall also fill all vacancies occasioned by death, resignation or removal which may occur while the general assembly is not in session; but all such appointees shall continue in office only until the meeting of the general assembly next thereafter, and until their successors be appointed and qualified. All vacancies which may exist at or during the meeting of the biennial sessions of the general assembly, caused by death, resignation or removal, shall be filled in like manner as those created by the expiration of official terms, and shall be only for the unexpired time of the party whose vacancy is thereby filled.
§ 172.050, RSMo