The original trustees having been appointed for terms of one, two and three years, respectively, the county boards of education shall, during the first week of April in each year, appoint one trustee for each district from the qualified electors and taxpayers residing in the district for which the appointment is made to succeed the trustee whose term expires during that year and to serve with the holdover members until his successor has been appointed and qualified.
S.C. Code § 59-19-30