Kingdom of Mountain and Vale - House Arryn
Ruler: Robyn Arryn; The Vale is a part of the six kingdoms
Kingdom of the Reach - Unknown
Ruler: Bronn; Highgarden is part of the six kingdoms; Bronn was given highgarden as payment of the Lannister debts.
Kingdom of the Stormlands - House Baratheon
Ruler: Gendry Baratheon; The Stormlands are a part of the six kingdoms
Principality of Dorne - Unknown
Prince of Dorne; Dorne is a part of the six kingdoms
Kingdom of the Rock - House Lannister
Ruler: Lord Tyrion Lannister; the Westerlands are a part of the six kingdoms; Tyrion is the hand of the king.
Kingdom of Isles and Rivers - House Tully
Ruler: Edmure Tully; The Riverlands are a part of the six kingdoms
Iron Islands - on/off part of Riverrun - House Greyjoy
Ruler: Yara Greyjoy; The Iron Islands have been a part of the Kingdom of Isles and Rivers on and off but mostly independent throughout history.
Kingdom of the North - House Stark
Ruler: Sansa Stark; Independent kingdom of its own with almost all of the north pledging their allegiance to Winterfell
Other Major Houses
House Targaryen - Undecided with Jon out in the wild and the 7 kingdoms not yet knowing his true parentage.
House Tarly - Ruler: Samwell Tarly; Hornhill (The Reach) is sworn to Highgarden; from S8E6 voting scene, it's clear that Sam is in charge of Hornhill.