Kan. Stat. § 19-303
If a vacancy in the office of county clerk should occur by death, resignation or otherwise, the vacancy shall be filled by appointment of a qualified elector of this state in the manner provided in this section. If the vacancy occurs on or after May 1 of the second year of the term, the person so appointed shall serve for the remainder of the unexpired term and until a successor is elected and qualifies. If the vacancy occurs before May 1 of the second year of the term, the person appointed to fill the vacancy shall serve until a successor is elected and qualified at the next general election to serve the remainder of the unexpired term. Nomination and election of such successor shall be in the same manner as nomination and election of a county clerk for a regular term. Appointments hereunder shall be made in the manner provided by law for filling vacancies in the office of member of the house of representatives.
K.S.A. 19-303