I'm guessing that you have already received an extension of time to answer the complaint, and now you need extra time to respond to the plaintiff's discovery. Rule 6(b)
of the North Carolina Rules of Civil Procedure states:
(b) Enlargement. – When by these rules or by a notice given thereunder or by order of court an act is required or allowed to be done at or within a specified time, the court for cause shown may at any time in its discretion with or without motion or notice order the period enlarged if request therefor is made before the expiration of the period originally prescribed or as extended by a previous order. Upon motion made after the expiration of the specified period, the judge may permit the act to be done where the failure to act was the result of excusable neglect. Notwithstanding any other provisions of this rule, the parties may enter into binding stipulations without approval of the court enlarging the time, not to exceed in the aggregate 30 days, within which an act is required or allowed to be done under these rules, provided, however, that neither the court nor the parties may extend the time for taking any action under Rules 50(b), 52, 59(b), (d), (e), 60(b), except to the extent and under the conditions stated in them.
If the time for answering hasn't already expired, you can arrange informally with plaintiff's counsel to extend the time to respond to discovery. Otherwise, you can file a motion with the court for an extension of time. Since you haven't even responded to the complaint, I would imagine that you shouldn't have any trouble getting the extension. If the time period for answering the discovery has expired, then you need to file a motion.
A motion for extension of time should set forth:
(A) the specific number of additional days requested;
(B) the date to which the extension is to run;
(C) the extent to which the time for the performance of the particular
act has been previously extended; and
(D) the reason or reasons on which the motion is based.