The House of Grilka was the new name given to the House of Kozak in 2371, after Kozak was killed in an accident on Deep Space 9. Gowron and the Klingon High Council granted Grilka [[[special dispensation]] to lead the House, as Kozak had died in an accident. (DS9: "The House of Quark")
The House of Grilka was involved in the Second Federation-Klingon War and the Klingon-Cardassian War. These conflicts were costly to the House, as they lost starships, lands and warriors. (DS9: "Looking for par'Mach in All the Wrong Places")