In short, I think she is going to be given a mission in Westeros, but the target is probably going to be someone who will divert her from the “no one” path and resume her identity as Arya Stark. I think the most appropriate target assigned to her will be Jon Snow because he has escaped “Death”, also known as the Stranger and the Many-Faced God by the Faceless Men. I think it would make sense for Jaqen to assign such a target to: 1) prove Arya is no longer Arya and 2) get vengeance for the death that was stolen from the Many-Faced God. I expect her to retrieve Needle from its nook in the wall and to come to Jon’s aid at Winterfell.
I would love to say she’ll kill Ramsay, but an assassination of Ramsay seems so cheap. I think he’ll have a more public death, almost certainly at the Battle of Winterfell. However, if he manages to escape Winterfell and hide with the Freys, for example, then this would be where Arya would come into the picture.
ARYA UPDATE: After seeing episode 5, the series creators have thrown unpredictability into the mix about why she will leave the Faceless Men. It seems just a reminder of her past and how the public viewed her father and sister may be enough to cast shade on her anonymous ambitions. Ultimately, it’s the people remaining on her list and her bonds to her family that will break her from this employment. What’s really ominous about episode 5 though, was Jaqen’s statement that “one way or another, a face will be added to the hall.” The organization is spread across the world, from what I understand, so she can’t just kill the Waif and Jaqen to get out of these obligations. They need to either allow her to peacefully exit or no matter what she does, they will eventually collect her face. Where is this going to go? I hope she is useful to the Stark plotline, but sometimes, the showrunners feel that a random death is useful to their storytelling. If the series allows her to escape Braavos, she could have a really interesting series of scenes in Westeros where she kills lots of people (similar to how Jaqen helped her escape from Tywin’s camp). However, given what the series creators did with Hodor, I feel they are just as likely to kill her cheaply to advance the inescapability of fanatics in GoT. END ARYA UPDATE