The Klingon restaurant was a small eatery opened on the Promenade of Deep Space 9 in 2370. The restaurant featured authentic Klingon cuisine prepared live by a master Klingon Chef who also serenaded his guests with traditional Klingon drinking songs.
Julian Bashir took Melora Pazlar to the Klingon restaurant in 2370, where she impressed the chef by her knowledge of Klingon food. Later that year, Jadzia Dax took her Trill initiate Arjin to the restaurant, though he was somewhat leery of the racht. (DS9: "Melora", "Playing God")
When Doctor Bashir and Garak met for lunch in the replimat they saw it was more than full and considered Quark's. But Garak was not in the mood for this noisy and crowded establishment and Doctor Bashir also excluded the Klingon restaurant. (DS9: "The Wire")
Jake Sisko, Leanne and Orak had dinner at the Klingon restaurant in 2371 where Leanne had ordered the gagh. A few weeks later, Leanne asked Jake if he would be willing to have dinner with her at the same restaurant. He agreed, but they decided to skip the gagh. (DS9: "Life Support")