Black Hawk is a Kai Grand Master.
Black Hawk is one of four Kai Masters (along with Star Lynx, Blazer and Steel Hand) assigned by Firestone (the second-most senior Kai warrior, after Lone Wolf) to apprehend Wolf's Bane. They successfully find Wolf's Bane, but are paralyzed by a powerful illusion conjured by the imposter. They are presumably released after Lone Wolf accepted Wolf's Bane's challenge to a duel.
By the events of The Storms of Chai, Black Hawk had risen to the level of a Kai Grand Master. Together with the other Kai Grand Masters, Lone Wolf assigned him to a dangerous mission. Black Hawk's mission was in the ruins of Cragmantle. At the end of the book it's mentioned that Black Hawk (and Swift Sword) did not return from his mission.