House Arryn
The purest blood of Andal kings, Wardens of the East, enthroned in the Eyrie above the Vale. They keep their own counsel in this age, as in most.
The fuller tale
The Arryns hold the oldest claim among the Andal houses to actual Andal blood, and the Eyrie has sat above the Vale since those first invaders crossed the narrow sea in numbers the First Men could not turn back — a pedigree the family wears the way other houses wear gold, which is to say, without feeling any pressing need to explain it further.
As High as Honor is not merely a motto in the Vale; it is closer to a description of the geography, since nothing reaches the Eyrie except by the Bloody Gate and a mountain road the hill clans have always been better at surviving than any army sent against them. It has made the Vale, across most of its history, a kingdom that answers when called and otherwise mostly forgets it is part of a larger realm at all.
In Daeron II's reign that pattern holds exactly true. No Arryn lord features in the tales' great crises — not the Ashford trial, not the Whitewalls conspiracy, not the Greyjoy raids — because the house keeps its own counsel in this generation as it has in most others, a policy less of hostility than of simple, mountain-bred indifference to whatever the lowlands happen to be arguing about this decade.
The page and the screen
House Arryn has no on-screen presence in the aired season and no confirmed role in any announced future one; the novellas mention the Vale only in passing, and the wiki's picture of this era's Arryn lord is drawn almost entirely from the wider Targaryen-era history rather than any Dunk and Egg scene.