Neb. Rev. Stat. § 39-1607

If any trustee fails to qualify within sixty days after receipt of the certificate of election, the office to which he or she was elected shall be declared vacant. Any vacancy in the board of trustees from any cause may be filled by the remaining trustees until the next election pursuant to section 39-1606 . At such election a trustee shall be elected by the voters of the district for the balance of the unexpired term of such trustee, if any.