Grilka was a Klingon woman of the House of Grilka in the 24th century Klingon Empire. She was from the Mekro'vak region on Qo'noS. She was married to Kozak, though was widowed. Her most trusted adviser was Tumek.
After Kozak died in Quark's in early 2371, Quark took credit for killing her husband, even though Kozak actually fell onto his own knife. She forced Quark to marry her so she could retain control of her house. Despite Grilka's aversion to matters of finance, she allowed Quark to inspect her family ledgers where he discovered that D'Ghor, Kozak's enemy, had been systematically attacking the House of Kozak for five years in order to weaken it. Quark, in turn, appeared before the council presented a report of his findings. The council quickly grew weary of Quark's report; but heard enough to be certain of D'Ghor's guilt.
Such an indirect and deceptive attack was highly dishonorable and Grilka demanded Quark confront the High Council with evidence of D'Ghor's deceit, which was tantamount to challenging D'Ghor to a duel to the death. Instead of fighting, however, Quark refused to defend himself, declaring that to 'fight' D'Ghor might as well be Quark's execution. D'Ghor was all too willing to strike Quark down, and nearly did, but for Gowron's well timed interference. Gowron was thus convinced of the accused Klingon's guilt and had him discommendated on the spot. With D'Ghor out of the way, Grilka was granted control of her house by Gowron and the House of Kozak became the House of Grilka. She divorced Quark (at his request) on the spot. (DS9: "The House of Quark")
In early 2373, Grilka visited Deep Space 9 again, along with Tumek and Thopok. The recent war with the Federation had been very costly to her house in ships, lands, and warriors. Though she feigned opposition to his request, she allowed Quark another opportunity to help her house by examining their records. This time, however, Quark's interest was truly stirred by the "glorious" Grilka.
At the same time, Worf, who had been assigned to the station the year before, also took an interest in Grilka. He attempted to pursue her as a mate but Tumek confronted him and advised him it was a waste of time. Worf's siding against the Empire during the war had stripped his House of its title and Worf of his honor; it would be unthinkable for Grilka to mate with him.
Upset by his failure, and Tumek's insinuation that he could not know anything about pursuing a Klingon woman because he had been raised among Humans, Worf decided to help Quark win Grilka's heart. He was successful by tutoring the Ferengi in the traditions of Klingon courtship. Grilka was warmed by Quark's efforts, even if she considered him a poor fighter. But Thopok was enraged by the prospect of a Ferengi pursuing a great lady and challenged Quark to a duel. With additional help from Worf, Quark defeated Thopok and Grilka welcomed his advances enthusiastically. (DS9: "Looking for par'Mach in All the Wrong Places")
Background information Edit
Grilka was played by Mary Kay Adams.
Adams commented on the character, "So many times in Hollywood, or in show business in general, women are not really allowed to be strong. We are tempered. Our power is taken away. Playing the Klingon woman was such a joy because throughout my entire career I have had directors say to me, 'OK, Mary Kay, just pull back a little bit.' This was the first time I was ever told, 'OK, we need you to be stronger!' It was Christmas! It was such a gift to be able to take it to the hilt and not be self-conscious like you can be in other roles. You're worrying, 'Uh-oh, they're going to be afraid of me now!' If you are a strong woman, you're labeled a bitch, or threatening, or difficult, or temperamental, or a whole lot of other things." 
L'Rell actress Mary Chieffo praised the characterization of Grilka, commenting, "I... really loved in Deep Space Nine Grilka. I loved her story with Quark and just how she ended up having to – she worked the system, and she was able to become the leader of her own house, which was, you know it is a patriarchal species, and so that was thrilling particularly because I think L'Rell follows in that vein."  In fact, the actress named Grilka as her favorite Klingon female character. Chieffo went on to say, "Grilka is definitely at the top, first of all, because she's full Klingon [....] Certainly for me, since L'Rell is full Klingon, seeing Grilka, I love her story of eventually becoming the leader of her own house. Klingons are so patriarchal, so that was a great way to explore that story, in both episodes that she's in. Her relationship with Quark was so fun and wonderful, and she just owned herself in this great way. There's something about that I've tried to transfer to L'Rell, and it's that her strength and power don't negate her sensuality. Grilka is the one that really always comes to mind." 
In Star Trek Online, Grilka took J'nek (β), a warrior on her ship during the Dominion War, as her mate. J'nek was killed in action late in the war, but not before Grilka became pregnant with her daughter Koren (β). Grilka then became romanticly involved with Worf in 2385, and married him a year later. They had a son, K'Dhan (β), in 2388.