The majority of Westeros must be in absolute disarray by the end of the season seven. With the passing of Olenna Tyrell and Ellaria Sand, both The Reach and Dorne are leaderless. The state of Casterly Rock is once again unknown in The Westerlands, and the Stormlands haven't even been a factor in anybody's decision making since the demise of Renly Baratheon back in season two.
Nobody seems particularly concerned about this possible anarchy, or the situation in the Riverlands after the ruling House Frey were all slaughtered at Arya Stark's hand. Control could have passed to Roslin Frey given that her infant son may have been the only male member of the house that wasn't killed, or nominal rule could've reverted to Riverrun and her husband Edmure Tully, assuming he was once again released from captivity after his captor's demise.
Edmure's defining attribute on screen has always been cowardice and ineptitude, evidenced by his momentary release in season six solely to order the surrender of the castle of Riverrun, which his uncle Brynden had been holding against all odds. In the books his actions are more heroic, and he surrenders the castle only after delaying long enough for the Blackfish to escape.
Both presumably have a part to play in the Winds of Winter and beyond, but in the truncated television adaptation it seems that Edmure is done without any of his remaining family batting an eyelid.
The Brotherhood Without Banners were amongst the series' longstanding absentees that resurfaced in season six, where Beric Dondarrion and Thoros Of Myr took The Hound into their still sizable ranks. By the time they played a part in season seven's excursion beyond the Wall, only the three of them remained and the question about what happened to the rest of their number wasn't asked or answered.
Bar a number of new individuals (with the exception of book character Lem Lemoncloak) that were introduced in the sixth season to depict the descent of elements of the Brotherhood into banditry, the only member bar Beric and Thoros ever specifically identified on screen was Anguy, who was by the pair's side throughout their season three narrative.
Disappearing during the three season gap between their appearances, Anguy hasn't been acknowledged as dead or as having deserted, so it can only be assumed that he was forgotten about (and that the audience wouldn't notice) or that the actor wasn't available.
Anguy is an almost anonymous member of the Brotherhood in the books, so it's intriguing that he was used as a composite of the various supporting players such as the aforementioned Lem and Tom O'Sevens. His only moment of note actually occurred two books before the Brotherhood rose to prominence, as he won one of the tournaments held to honour Ned Stark's appointment as Hand of The King.