I'm pretty sure that Azir will try to reclaim his lost territory, but I doubt that he'd directly attack Noxus, especially since he'd either need to go there by ship or conquer Piltover/Zaun first, which will be difficult on its own.
Though I'm not sure what Noxus will do, Swain might try to negotiate with Azir first, but I doubt that Azir would be willing to give Noxus anything that he considers to be Shuriman territory/property.
Cassiopeia is a wild card in all of this though, she'd likely try to get close to Azir to manipulate him, but her new appearance should be a dead giveaway to Azir that she is no one that should be trusted(especially after what happened with Xerath), so this would prove difficult, if not impossible for Cassiopeia.
So I wonder if she might not try to get on Xeraths good side instead, though that'd be dangerous for her out of entirely different reasons.