Tararat was reluctant. Ackster had brought him and the dragonling race nothing but trouble. But, on the other hand, Ackster had also given them a chance to make peace with the Dragon Slayer and save their race from an early extinction.
At first, the dragonlings wanted to chase Kargas down when he left the Council meeting since it was his fault the dragons were up and about. However, the way he had beaten all the challengers and even stood up against a dragon, albeit less successfully than Ackster, made most dragonlings reconsider.
Tararat was not among those. He saw the destruction and potential of Kargas. He also saw the loathing in Kargas' eyes when he looked at Killgara and some of the dragonlings. He couldn't leave such a threat alone. So, he went after Kargas.