Kan. Stat. § 25-2022
Any board shall have power to fill by appointment any vacancy which occurs thereon, and such appointee shall serve for the unexpired term. When a vacancy occurs, the board shall publish a notice one time in a newspaper having general circulation in the school district stating that the vacancy has occurred and that it will be filled by appointment by the board not sooner than 15 days after such publication. If such vacancy occurs before May 1 of the second year of the term leaving an unexpired term of more than two years such appointee shall serve until the second Monday in January after the following general school election as provided in K.S.A. 25-2023, and amendments thereto.
In the latter event, the unexpired term of two years commencing on the second Monday in January after the following general school election shall be filled at such election and the ballots or ballot labels and returns of election with respect to such office shall be designated as follows: "To fill the unexpired term."
K.S.A. 25-2022