For quite some time people had ceased to seriously believe in White Walkers. During that time the Night's Watch continued to exist, serving two purposes:
- Ward off Wildlings the best they can
- Be a politically convenient dumping ground for criminals etc.
No reason it can't continue to do this. The first one is all the more relevant now that there's a big hole in the wall. And there's a shot at good political relations with them now, which would transform the first into the political function of preserving and monitoring those relations.