K'Vada was an officer in the Klingon Defense Force, a captain by rank. In 2368, he commanded a Bird-of-Prey that covertly transported Jean-Luc Picard and Data to Romulus to investigate the presence of Ambassador Spock on that planet.
He goaded Picard by assigning him a cramped, uncomfortable berth aboard his ship and warning him that no "Federation food" would be served on the voyage. Picard did not rise to the bait. K'Vada laughed out loud when he saw Picard and Data disguised as Romulans, and jokingly told Data to be careful, as some Romulan woman might take a liking to him and get close enough to see through his disguise. He also told Picard that, once he and Data were on the planet, they would be on their own, as his orders did not include trying to rescue them from the planet's surface.
He subsequently gave Data grudging permission to use the Klingons' computers to attempt to infiltrate the Romulan data banks. (TNG: "Unification I", "Unification II")
Apocrypha
K'Vada's backstory is expanded in the novelization. He has a wife, K'Kam, with whom he has had a violent argument shortly before his assignment, who has emphasized her points by dislocating his shoulder. Thanks to his ship's surgeon's ineptitude, the injury has not healed properly, which accounts for his foul mood. He begins to think better of his assignment, and his passengers, after Data notices his distress and properly treats the injuries to his arm. He is also enthralled at the idea of Data gaining access to the Romulans' data banks, though he is careful to conceal it. Having seen Data's abilities, he plans to sponsor a research initiative into creating androids for the KDF once he returns. By the end of the mission, he is well-satisfied and is anticipating praise from his superiors and the awe of his wife.
K'Vada also appears in the IKS Gorkon novel Honor Bound. In it, he is the recently-assigned captain of the cruiser IKS Vidd and a member of the Order of the Bat'leth, formed by the Lady Lukara after the death of Kahless the Unforgettable to uphold Kahless' vision of Klingon honor. The Order is rallied by Captain Klag of the IKS Gorkon to battle against General Talak, who has ordered Klag to break an honorable agreement with a people known as the Children of San-Tarah. K'Vada is one of the members who answers the call, and dies in glorious battle against Talak's fleet in orbit of San-Tarah, ramming his crippled vessel into the enemy cruiser IKS Gogam.