A kingsmoot gave to House Hoare the Seastone Chair after the Greyiron line had been extinguished. However, instead to return back to the Old Way when all the kings were chosen in assembly, the Hoares kept the title hereditary as the Greyirons had done.
Under King Qhored Hoare the realm of the ironborn reached the peak of its expansion, and it was said that all the western coast of Westeros were the salt of the sea could be smelt or hear the crashing of waves were under their control. Although it is unlikely that this assertion is literal, since with all probability places like Oldtown or Lannisport have never been ruled from the Iron Island, it is still remarkable that the ironborn could hold places as distant as the Arbor.
During the next years, the power of House Hoare would disminish and many of the conquests would be lost. The Bear Island was lost to Rodrik Stark in a wrestling, who gave it to the Mormonts. The possessions of the ironborn were reduced to the Isles and the coast of the rivelands.
In a new age of expansion, the ironborn took the all the riverlands from the Storm Kings (who had killed the last River King 300 years before). Harren the Black ordered the construction of Harrenhal, the greatest castle of the Seven Kingdoms, at the shores of the Gods Eye long away from the sea. The construction took forty years, and was finished the day Aegon and his sisters landed Westeros. Having seen how Kings Loren and Mern had been defeated at the Field of Fire, he decided to remain at his castle. Aegon burned it with his dragon, burning alive Harren and his sons thus ending the Hoare line.
According to non-canon letters from George R. R. Martin, his banner depicts per saltire and with two heavy silver chains crossing between a gold longship on black, a dark green pine on white, a cluster of red grapes on gold, and a black raven flying in a blue sky (clockwise). His banner represents all the distant lands that had been under the rule of the house: the longship for the Iron islands, the green pine for the Bear Island (the northenest border of their dominion), the cluster for the Arbor (the southernmost) and the black raven for Raventree Hall on the RIverlands; all bound by the iron chains of the ironmen.
Harrag Hoare is cited by Aeron Damphair as an example of a great king that was chosen through a kingsmoot. Possibly he was the one chosen after the death of the Greyiron line, but he could also had been a previous King from the same house.
The house reached the peak of its power under King Qhored, but his descendants started to lose possessions.
Harren the Black was the last Hoare king. He was burned alive with his sons at the Kingspyre Tower from Harrenhal.
During the timeline were the events of A Song of Ice and Fire take place, there's a man from the isles named Harren Half-Hoare, whose connection to House Hoare is not referred to. He supported Euron Greyjoy during the kingsmoot.