House Drumm was in service to House Hoare during the reign of Qhorwyn Hoare. After the Kingsmoot elected his formerly banished son Harwyn Hoare as King of the Iron Islands, he gathered the armies of the Iron Islands, including those of House Drumm and House Harlaw and attacked the mainland of Westeros.
In the books
The Drumms own a Valyrian steel sword, Red Rain, which was taken from a knight years ago by Hilmar the Cunning with wits and a wooden cudgel. Due to the name and the color of the sword, it is possible the sword belonged to House Reyne.
The Drumms hold the title "Lord of Old Wyk", suggesting they have some type of sovereignty over the whole island and its other houses, such as the Stonehouses. During the Greyjoy Rebellion, the Drumms would have commanded the defense of their island against the host led by Ser Barristan Selmy.
When Theon Greyjoy arrives at Pyke, Aeron Greyjoy tells him Dagmer Cleftjaw has gone to Old Wyk to summon the Stonehouses and the Drumms.
Lord Drumm's ship, Thunderer, is spotted by Victarion Greyjoy on Old Wyk's shores for the kingsmoot. Lord Dunstan Drumm claims the Seastone Chair for himself at the kingsmoot, his champions being his sons, Denys and Donnel Drumm, and Andrik the Unsmiling. Aeron thinks his champions are notable and Dustan starts speaking well. However, he fact that he talks too much of his family's past glories, and that the contents of his chests only contain bronze, diminish his support. Lord Dunstan wears Red Rainduring the kingsmoot.
After the Battle of the Shield Islands, Victarion sees Rodrik Harlaw, Gorold Goodbrother and Dunstan Drumm talking in the yard of Oakenshield. King Euron Greyjoy names Andrik Lord of Southshield after the conquest of the Shield Islands, a move that is understood by Victarion as a strategy of depriving The Drumm of his strong right hand.