RogueOne
I do struggle to think of any. Most of the old profitable routes have been jumped on by other airlines and they're too thin to require two airlines competing against each other. There's probably a very good reason other airlines haven't jumped on the other routes.
This new airline will no doubt at some point be subject to a TUPE claim. And a new airline will not want the old airline's pilot agreements shackled to them.
As BA318 points out, where is the niche? What will set them aside to make them attractive over other airlines to pax?