[WARNING – This article contains SPOILERS for Game of Thrones season 6.]
With 'The Winds of Winter,' the season 6 finale, Game of Thrones gave fans arguably the most satisfying and cathartic ending to any single season of the show. Following the events of 'Battle of the Bastards,' in which Sansa Stark got her glorious and poetic vengeance against Ramsey Bolton by loosing his own starved dogs on him, the season 6 conclusion extended the theme of terrible people finally getting their comeuppance. While Cersei Lannister racked up the biggest body count of the episode by far, it was Arya Stark who had the most meaningful kill for long-suffering fans of the show: the stealthy and gruesome assassination of Walder Frey after he feasted upon a hot pie made of his sons.
Arya's journey to becoming the capable, cold-blooded assassin who finally ended the long, bloody, and perverted rule of Walder Frey was a slow and methodical one, a story weaved throughout the tapestry of the show since season 1. George R.R. Martin is a very patient storyteller, perhaps too patient for those awaiting the next book in his Song of Ice and Fire series, but with Game of Thrones' showruners running out of source material and having to flesh out Martin's notes themselves, it is starting to feel like they are putting the pieces in place to bring an end to the tale of Westeros. No doubt many fans were well and truly ready to be done with interminable scenes of Arya training with the Faceless Men, but those who stuck around finally got their reward.
With Arya finally breaking free of the Faceless men and becoming a skillful assassin in her own right, the question for the seasons to come is whom she will kill next. Her hit list is a long one, although shorter for the TV show than in the books: Joffrey, Cersei, Walder Frey, Meryn Trant, Tywin Lannister, the Red Woman, Beric Dondarrion, Thoros of Myr, Ilyn Payne, The Mountain, and the Hound. Some on that list have died by someone else's hand, some remain living, and one of them is some sort of horrifying undead abomination. To figure out whom Arya might strike next, the first step is to eliminate those who are already gone.
Joffrey met his end during the 'Purple Wedding' in season 4, episode 2, 'The Lion and the Rose,' marking the first truly cathartic death of the show. His grandfather Tywin met his inglorious end via crossbow at the hands of Tyrion while sitting on the john at the end of season 4. Arya herself managed to off Meryn Trant herself after spotting him in Braavos during the season 5 finale. She likely assumes the Hound is dead, having left him to die on his own, but of course it was learned recently that that's not the case.
Even if Arya does encounter the Hound again, it seems like her hatred for him has mostly passed. They nearly became friends, but for the fact that she left him for dead. In addition, the likelihood that she could take out his now-undead brother the Mountain is pretty low given his current condition, so that leaves the following: Cersei, the Red Woman, Beric Dondarrion, Thoros of Myr, and Ilyn Payne. Given that Beric Dondarrion and Thoros of Myr are now in the company of the Hound, one strong likelihood is that Arya encounters the three of them and leaves only one remaining. Or perhaps she's really serious about this whole murdering thing and takes out the Hound after all.
Ilyn Payne is ostensibly still out there somewhere, but is so inconsequential at this point that it would almost seem like a waste of screen time to show Arya pursuing him. Then again, it just might happen for the sake of wrapping up loose ends. The big targets, though, are Cersei and the Red Woman, a.k.a. Melisandre. Both have done some pretty monstrous things, although Melisandre's edges softened considerably in season 6 (and that's not just a reference to her true age). If Arya could take out one or both of them, that would be the sort of big, shocking moment on which Game of Thrones has built its reputation.
So given all that, who is likely to be Arya's next target? Her story has been building for a long time, and the clearest path forward would be to let it continue to build. That means that her next target is unlikely to be someone as big as Cersei or Melisandre. They might very well come later, but first she needs to cross some of the lesser names off her list. That might be Ilyn Payne, but if so then it would likely be in a throwaway moment like in the cold open to an episode. The next major plot point for Arya is likely to be her crossing paths with Beric Dondarrion, Thoros of Myr, and the Hound. Her reunion with and possible killing of the Hound would bring their story full circle, and with Beric and Thoros present as well it could provide the opportunity for a rousing and bloody three-way battle. The story arcs of Arya and the Hound are mirror images of each other: she tried to go full-on, remorseless assassin and came up short, whereas he tried to leave killing behind and came up even shorter. That kind of story parity is no accident.
Once the encounter with those three is out of the way, Arya may join her brother and sister in the newly recaptured Winterfell, or she may just go on killing. The houses of Stark, Lannister, and Targaryen are converging for what promises to be some amazing final battles to determine who is ultimately left ruling Westeros, with the wild card being when and how the White Walkers will strike. No character is safe in Game of Thrones; that ground rule was established with Ned Stark's death back in season 1. There are few left standing, though, who are as tough as his daughter Arya.
Game of Thrones will return to HBO with season 7 in spring 2017.