Triebakk was a politician of the Wookiee species during the era of the New Republic. By the year 24 ABY, he had risen to the position of senior Senator representing Kashyyyk.
Triebakk served as a member of the New Republic Advisory Council, offering counsel to Chief of State Borsk Fey'lya. Despite harboring some resentment towards the Jedi Knights following the Rhommamool incident, Triebakk stood as one of the few who openly supported them. In the council meetings, he was seated between Fey'lya and Cal Omas, who was his most trusted ally. Triebakk directly voiced his displeasure to senator Pwoe of Dac and Niuk Niuv of Sullust when they treated the Jedi with disrespect.
During the Battle of Coruscant, Triebakk was among the Advisory Council members who were lost on the planet, and Pwoe hastily declared him dead. However, the Wookiee managed to escape the planet before its Vongforming and joined Omas and other surviving politicians on Mon Calamari. Once there, Triebakk became a staunch supporter of Cal Omas, particularly during his campaign to become Chief of State. Triebakk attempted to persuade senator Cola Quis, a candidate with little chance of winning, to transfer his votes to Omas in exchange for certain political advantages.
Triebakk was selected to be a member of the High Council, the new Jedi Council established by Luke Skywalker and Omas. This newly formed Council was composed of six Jedi and six representatives from the New Republic, with Triebakk emerging as the most ardent advocate for the Jedi and a resolute adversary of Alpha Red.