What do expect will happen with littlefinger

He's not doing much, is he? Personally, I expected him to haul south and take over the Riverlands, put Edmure back in charge and use him as a puppet lord, like he's using Robyn and is trying to use Sansa and Jon. But he's not, he's just sitting around Winterfell, and maybe the guy on another forum who said that he's waiting to see whether Dany or Cersei wins is correct.

if that's his plan, he should do his waiting in the Vale, away from Arya and Bran. Bran can tell Arya that he was behind Ned's arrest and execution, and Arya can take him out any time. And Sansa, the woman he loves and whom he's taught everything, will probably react to that by telling Arya they still need the Vale knights and please let her know about any assassination plans next time.

nothing, the show follows most of his plans from the books which now have diverge too much that nothing he does feels like hes ahead of the game ever since he made Sansa marry Ramsey.

He's gonna try to pit the Stark kids against each other. He won't be very pleased that neither Bran nor Arya want the lordship of the Winterfell like Sansa does.
He'll even plant the old letter from Sansa (dictated by Cersei) to Robb for Arya to find.
Arya will think that Sansa is a traitor for a little while but Sansa isn't that stupid anymore.
She'll quickly figure it out and let Arya know who the real traitor is.
Then Arya will execute him on Sansa's order.
The End.
I hope you don't miss him but his days are numbered.

I think he thinks he has two new weapons to manipulate. He tried to win over the boy by giving him a gift so he can use his powers. And he was grinning when he saw Arya fighting thinking he now has a weapon he can manipulate to into doing what he wants.

I think his goal changes as power shifts. I think when it suites him and if Daenerys Targaryen is about to take control he will declare his support in exchange for being declared the Warden of the West and getting Sansa hand in marriage.

I think he will try to use Arya and Bran as a way to undermine John Snow in the North.

Seeing that the scripts have been leaked......it's quite obvious what's going to happen to him. If I were him I would leg it as fast as possible before the end of Episode 7.

Arya will gut him.

littlefinger will become king. all of this is because of him. its all his big plan.