N.C. Gen. Stat. § 160A-63
A vacancy that occurs in an elective office of a city shall be filled by appointment of the city council. If the term of the office expires immediately following the next regular city election, or if the next regular city election will be held within 90 days after the vacancy occurs, the person appointed to fill the vacancy shall serve the remainder of the unexpired term. Otherwise, a successor shall be elected at the next regularly scheduled city election that is held more than 90 days after the vacancy occurs, and the person appointed to fill the vacancy shall serve only until the elected successor takes office. The elected successor shall then serve the remainder of the unexpired term. If the number of vacancies on the council is such that a quorum of the council cannot be obtained, the mayor shall appoint enough members to make up a quorum, and the council shall then proceed to fill the remaining vacancies. If the number of vacancies on the council is such that a quorum of the council cannot be obtained and the office of mayor is vacant, the Governor may fill the vacancies upon the request of any remaining member of the council, or upon the petition of any five registered voters of the city. Vacancies in appointive offices shall be filled by the same authority that makes the initial appointment. This section shall not apply to vacancies in cities that have not held a city election, levied any taxes, or engaged in any municipal functions for a period of five years or more.
In cities whose elections are conducted on a partisan basis, a person appointed to fill a vacancy in an elective office shall be a member of the same political party as the person whom he replaces if that person was elected as the nominee of a political party.
N.C. Gen. Stat. § 160A-63
Town of Tabor City, 2013 N.C. Sess. Laws 8, s. 1