Triebakk became a member of the New Republic Advisory Council, advising Chief of State Borsk Fey'lya. Triebakk was one of the minority which openly supported the Jedi Knights, despite a strong disgruntlement with them after the Rhommamool incident. In the meetings he sat between Fey'lya and Cal Omas, his closest ally. Triebakk complained directly to senator Pwoe of Dac and Niuk Niuv of Sullust when they were rude to the Jedi.
During the Battle of Coruscant, Triebakk was one of the Advisory Councilors lost in the planet, and Pwoe quickly declared him dead. However, the Wookiee somehow succeeded in leaving the planet before its Vongforming and he joined Omas and other surviving politicians on Mon Calamari. Once on Mon Calamari, Triebakk was a firm supporter of Cal Omas, especially when he tried to become the Chief of State. Triebakk tried to convince senator Cola Quis, a candidate without a real chance to win, to give his votes to Omas in exchange of some political favors.
Triebakk was chosen to be a member of the High Council, the new Jedi Council formed by Luke Skywalker and Omas. This new Council consisted of six Jedi and six New Republic representatives, of which Triebakk was the strongest supporter of the Jedi, and a determined opponent of Alpha Red.