1st get your new DL which you can go online
https://www.ncdot.gov/dmv/ and just do a change of address and have it mailed to your new address (change your vehicles registrations at the same time too). After you receive your new DL go to issuing Sheriff and do address change ... they will give you an address change paper you must carry with you new DL and current CHP. Next if you want you can go to your new Sheriff and you can request a replacement CHP with new address (I think $15) which he’ll issue after receiving your file from your previous Sheriff ... expect this to take a few weeks. When it comes time for renewal the new Sheriff will have your file and renewal will be same as before.