SDCL § 9-13-41: Election day transition--Term of office.

If a municipality schedules a regular election on the first Tuesday after the first Monday in November, the term of office for each office holder whose term was to expire earlier in that year must have the term extended until the office holder or another candidate for the office is duly elected and qualified.

If a municipality schedules a regular election on the first Tuesday after the first Monday in June to elect an office that was previously elected in November, the office holder who was elected in November is entitled to complete the term of office to which the office holder was elected.