Kozak was the head of the Klingon House of Kozak in the latter 24th century. He was fond of gambling and owed a large, unpaid debt to D'Ghor.
On a trip to Deep Space 9 in 2371, he spent his time in Quark's where he drank excessive amounts of bloodwine. After Quark told him he would get no more without paying, Kozak attacked the Ferengi in a drunken rage. However, due to his inebriation, he fell on his own knife, killing himself. Quark later said he had killed Kozak in self-defense, looking for a way to boost his number of customers.
Upon Kozak's death, D'Ghor tried to take over the House of Kozak, but was thwarted by Kozak's widow, Grilka, with help from Quark. The House of Kozak then became the House of Grilka.