I'm probably wrong, but I'm going to call it now: Dany and Jon both die, thus ending the Targaryen bloodline forever. That leaves the newly legitimized Gendry Baratheon, Lord of Storm's End, as the closest thing to a rightful heir to King Robert's throne who then recognizes the North as an independent kingdom under Queen Sansa's rule.
The realm could do far worse and Varys will not have died in vain.