California Code, Government Code - GOV § 24204

Whenever any county frames and adopts a charter for its government, which is approved by the Legislature, and the charter provides for the appointment of any officers of a county, the officers first appointed under the charter are the successors of the like elective officers in office at the time of the approval of the charter.  The elective officers shall continue to hold office for the term for which they were elected and until the appointment and qualification of their successors under the charter.  No election for any officer whose successor is to be appointed shall be had at any election held subsequent to the approval of the charter, except to fill a vacancy for an unexpired term.