Mo. Rev. Stat. § 249.180
In the event of any vacancy in the office of trustee caused by death, resignation, refusal to act or in any wise, such vacancy shall be filled by appointment made by the remaining trustee or trustees. In the event the remaining trustees cannot agree upon such appointment within thirty days after such vacancy may have occurred then such vacancy shall be filled by the appointment of the circuit court, and the trustees so appointed shall possess the qualifications for a trustee elected under the provisions of sections 249.010 to 249.420 and shall subscribe his oath or affirmation as if he had been elected. The trustee or trustees so appointed shall serve until the next election for trustee at which time a trustee shall be elected to fill such vacancy.
§ 249.180, RSMo