Wash. Rev. Code § 87.03.081
A vacancy in the office of director shall be filled by appointment by the board of county commissioners of the county in which the proceedings for the organization of the district were had. At the next annual election occurring thirty days or more after the date of the appointment, a successor shall be elected who shall take office on the first Tuesday in January following and shall serve for the remainder of the unexpired term.
A director appointed to fill a vacancy occurring after the expiration of the term of a director shall serve until his or her successor is elected and qualified. At the next election of directors occurring thirty days or more after the appointment, a successor shall be elected who shall take office on the first Tuesday in January next and shall serve for the term for which he or she was elected.
Failure on the part of any irrigation district to hold one or more annual elections for selection of officers, or otherwise to provide district officers shall not dissolve the district or impair its powers, where later officers for the district are appointed or elected and qualify as such and exercise the powers and duties of their offices in the manner provided by law.
RCW 87.03.081