New Mauville can be accessed during the Post Game.
After the Delta Episode, if you head to the center of Mauville City, Wattson should be there. Head to his Apartment after you talk to him. He gives you authorization to enter New Mauville. Nothing is in there for to the story whatsoever, due to it being accessed in the Post Game. There are certain Items located inside it, but I won't spoil them. If you want to know how to get there, head to route 110 and make sure you have a Pokemon with Surf.
Hope I helped!