N.C. Gen. Stat. § 1-567.45

(1) Where the mandate of an arbitrator terminates for any reason, a substitute arbitrator shall be appointed according to the rules that were applicable to the appointment of the arbitrator being replaced.

(2) Unless otherwise agreed by the parties: Where the number of arbitrators is less than three and an arbitrator is replaced, any hearings previously held shall be repeated;

(3) Where the presiding arbitrator is replaced, any hearings previously held shall be repeated;

(4) Where the number of arbitrators is three or more and an arbitrator other than the presiding arbitrator is replaced, any hearings previously held may be repeated at the discretion of the arbitral tribunal.

(5) Unless otherwise agreed by the parties, an order or ruling of the arbitral tribunal made prior to the replacement of an arbitrator under this section is not invalid because there has been a change in the composition of the tribunal.