What will be the role of Littlefinger in the upcoming season of Game of Thrones?

Erek:

Littlefinger has been angling for the Iron Throne, and I think eventually he will marry Sansa and become one of the biggest High Lords, but will eventually realize that he needs to step back from Jon and Dany.

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Matt: 

I don't believe Littlefinger will ever manage to marry Sansa. She rejected him in the Season 6 finale, and while he did help to save her, he has not properly endeared himself. His power is built entirely upon his wit and charisma, and is more borrowed than legitimate. I think he will continue playing his games, but in the end will run out of allies. I would not be surprised if he eventually tried to pit Dany against Jon, and in response Sansa exposes his murder of Lysa Arryn.

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Erek: 

That would be an interesting eventuality. In the books I feel like he falls more clearly on the hero camp even though he is a scumbag, but in the show he is more clearly a villain. But I think Sansa will marry for the Alliance ultimately. I also think she will realize she needs him and is more like him than she wants to admit.

Beyond his romantic fate with Sansa, I think he has a major role to play and can bring a political mind to the North. Jon doesn't understand politics much at all. So he needs Littlefinger for his network, his men, and even for his strategic mind.

 

Matt: 

I feel Sansa may actually go back to Tyrion. In both mediums though, Littlefinger is portrayed as a social climber who loved only Catelyn. His affection towards Sansa is frequently depicted as her being a stand-in for her mother. Regarding Littlefinger stepping to the side, he only does so when it is to his advantage, and considering his ultimate goal is the throne, I don't see him abandoning it.

Also to his disadvantage is that both Jon and Dany have counselors with extreme distrust as of Littlefinger with varying knowledge regarding his duplicity.

 

Erek: 

Littlefinger is insinuated into everything though. He knows everybody because of his role as the treasurer. People owe him favors all over and I think his love for Catelyn is a guide star that he follows that will work in Sansa's favor. 

Tyrion is a pragmatist who knows Littlefinger's value.

And right now Jon needs his swords.

 

Matt: 

I feel Littlefinger is slowly approaching his limits of gamesmanship. While he may stay loyal to Sansa, in the face of purely loyal forces such as Jon or Dany, he can't manipulate his way past them. His only card right now is the Knights of the Vale, and they aren't fully committed to him. I believe how he insinuates himself into the emerging groups will decide his fate, but I don't see him living for too much longer. The downside for playing the game too well is it makes a lot of enemies.

Also, Sansa deep down most likely remembers that he played a hand in the death of her father. I think this may come back to haunt him soon.