I think if a KHIII were to come out, it'd start afresh with a new main character.
Roxa’s will be long gone, Riku will be dead and Sora and Kairi will be at the Castle of Kingdom Hearts, as the new rulers of the lost kingdom of hearts.
The Heartless would be sealed away for a time in the hearts of people, but are not forever gone as with the Nobody’s, light and darkness are eternal.
They would still visit Destiny Isles now and again; the Keyblade however will have passed onto a new master, now that both the door to light and dark are now closed.
World travel is possible as the circumstances briefly said in the story of Grandma’s story were resolved at the Castle of Kingdom Hearts at KHII end, and the false leading ‘true light’ was revealed.
The XIII Order are no more, most were killed, maybe one got restored, I'm not so sure as of right now whom would deserve such a feat, but seeing as Axel is meant to be a sad and deep character... Zexion is more coolio though!
A new enemy would arise out of the chaos of the new world order.