ยง 2114. Filling vacancy in office of clerk, collector or treasurer.  A
  vacancy in the office of clerk, collector or treasurer, may be filled by
  appointment  by  the  trustees of the district, and the appointees shall
  hold their respective offices until  the  next  annual  meeting  of  the
  district, and until their successors are elected and have qualified.
Structure New York Laws
Title 2 - School District Organization
Article 43 - School District Officers--Town and County Officials
2102 - Qualifications of Officers.
2102-A - Required Training for School District Officers.
2103 - Ineligibility to Office.
2103-A - Police Officers and Firefighters on Boards of Education.
2106 - Terms of Officers of Newly Created District.
2108 - Notice and Acceptance of Election.
2109 - Refusal of Trustee to Serve.
2110 - Penalty for Refusal to Serve or Perform Duty.
2111 - Resignation of District Officers.
2113 - Filling Vacancy in Office of Trustee.
2114 - Filling Vacancy in Office of Clerk, Collector or Treasurer.
2115 - Notice of Appointment to Fill Vacancy and Filing Thereof.
2116 - District Records, Books, etc., Are District Property.
2116-A - Books and Records to Be Kept by School Districts.
2116-B - Internal Audit Function.
2118 - Expenses of School District Officers.
2119 - School District Trustee Not to Draw Draft on County Treasurer in Certain Cases.