Kan. Stat. § 15-201
Every two years an election shall be held for a mayor, and five council members. The mayor and council members shall hold their offices for two years and until their successors are elected and qualified.
Subject to the provisions of K.S.A. 12-16,128, and amendments thereto, in case of a vacancy in the council occurring by reason of resignation, death, or removal from office or from the city, the mayor, by and with the advice and consent of the remaining council members, shall appoint an elector to fill the vacancy until the next election for that office. In case any person elected as a council member neglects or refuses to qualify within 30 days after election, the council member shall be deemed to have refused to accept the office and a vacancy shall exist. Subject to the provisions of K.S.A. 12-16,128, and amendments thereto, the mayor may, with the consent of the remaining council members, appoint a suitable elector to fill the vacancy.
In case of a vacancy in the office of mayor, the president of the council shall become mayor until the next regular election for that office and a vacancy shall occur in the office of the council member becoming mayor.
K.S.A. 15-201