N.C. Gen. Stat. § 120-30.12
Vacancies in the appointive membership of the Legislative Research Commission occurring during a term shall be filled for the unexpired term by appointment by the officer who made the original appointment. Vacancies in the ex officio membership shall be filled for the unexpired term by election by the remaining members of the Commission. Every vacancy shall be filled by a member of the same house as that of the person causing the vacancy.
If for any reason the office of President pro tempore of the Senate becomes vacant, the five Senate members of the Legislative Research Commission shall elect one of their own number to perform and exercise the duties imposed and powers granted pursuant to this Article, and such Senator so elected shall serve until the Senate shall elect a President pro tempore. If for any reason the office of Speaker of the House of Representatives becomes vacant, the five members of the House of Representatives of the Legislative Research Commission shall elect one of their own number to perform and exercise the duties imposed and powers granted pursuant to this Article, and such member of the House of Representatives so elected shall serve until the House of Representatives shall elect a Speaker.
N.C. Gen. Stat. § 120-30.12