I think Euron will hook up with Cersei now that Dany's out. That would give Euron some character development while allowing the KL crew (which is now down to just Jaime, Cersei, and Qhyburn) to interact with somebody new. Plus, someone's going to have to take on Dany's massive fleet.
As far as the North goes, I suspect there will be some friction between Jon and Sansa. Sophie Turner said in an interview that Sansa was annoyed not to get more credit from the Northern houses and she now views LF as being more trustworthy. Hopefully this storyline doesn't end with her betraying Jon.
If that's true, then I really hope they develope that idea better in Season 7; there's no way to read Sansa's decisions without making huge guesstimations, and most people seem to think the point of her look to Littlefinger after the acclamation of Jon was one of worry for her half-brother/cousin. There was no jealous gaze directed at Jon, and while they made Jon be an idiot during the Battle of the Bastards, he was completely accommodating to Sansa's objections and worries the night before. If they want her to have jealousy, there should be more scenes showing her experiencing at least some discomfort with Jon's accolades.
However, if they do start to establish Snasa as giving into a few of Littlefinger's evil whispers, I do know who should be the advisor to help her overcome that: The Hound. Sansa doesn't just have trust for the Hound, she understands him; the show especially had Turner give him an almost epiphanic look when she realized he wouldn't hurt her during Blackwater. And the Hound, while not exactly philosophical, has a good head on his shoulders and a very good grasp of straightforward thinking and observation. Plus, considering the development the show gave the Hound and Arya, he probably figures that Snasa really should be trusting Jon more, since he knows the family's good.
And of course, he was there when Littlefinger put a dagger to Ned's throat...
Again, I'm not saying that the Hound will be the political advisor to Sansa. I'm saying that he'd make a fine consigliere to her, though, and she might realize she needs that.