In the 2150s decade, Doctor Antaak, a medical scientist, led this Great House. He was involved with the onset of the Augment Crisis that befell the Klingon Empire during failed medical experiments in the Qu'Vat colony in 2154. As a result, he became one of the first QuchHa' - Klingons with Human-like physiology. (ENT episode: "Divergence")
By 2409, the House of Antaak still carried the same name. In that year, a member of this house participated in the annual bat'leth competition on Forcas III. They brought an abundance of medical supplies.
The training room assigned to House Konjah was searched by Ambassador Worf, his son Alexander Rozhenko and a Klingon Defense Force officer for signs of collaboration with the Romulan Tal Shiar. The investigators did not turn up anything incriminating House Antaak. (STO - Warzone mission: "Bringing Down the House")
In the Kelvin timeline, House Antaak was active in the 23rd century. In the early 2260s decade, the house pursued an agenda separate of the Klingon Empire, and frequented star systems in the Neutral Zone from 2262 onwards. Their patrol ships included D4-class birds-of-prey (TOS video game: Fleet Command)