105 ILCS 5/5-14
Successors to the trustees whose terms of office expire at the time prescribed in Section 5-13, and their successors, shall hold their offices for 6 years and until their respective successors are elected and qualified. Trustees of schools shall enter upon the duties of their office on the third Monday of the month following their election.
Whenever a vacancy occurs, the remaining trustees shall fill the vacancy until the next regular school election, at which election a successor shall be elected to serve the remainder of the unexpired term. However, if the vacancy occurs with less than 28 months remaining in the term, or if the vacancy occurs less than 88 days before the next regularly scheduled election for this office then the person so appointed shall serve the remainder of the unexpired term, and no election to fill the vacancy shall be held. The successor shall have the same residential qualifications as his predecessor. Should they fail so to act, within 30 days after the vacancy occurs, the regional superintendent of the region in which the township lies, or if the township is divided by a county line or lines, the regional superintendent of the region in which a majority of the children, who reside in districts subject to the jurisdiction of the trustees of schools of such township, attend school, shall within 15 days after the remaining trustees have failed to fill the vacancy, fill the vacancy as provided for herein. The successor shall have the same type of residential qualifications as his predecessor.
105 ILCS 5/5-14