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.