In the mirror universe, the Vedek Assembly was the ruling council of the Bajoran religion. Following the conquest of Bajor by the Terran Empire in 2255, it was dissolved while the Bajoran religion was suppressed and driven underground.
After Iliana Ghemor became the Emissary of the Prophets in 2377, the Bajoran people converted to their long neglected religion en masse and the senior members of the underground religious movement came out of seclusion to reconstitute the Vedek Assembly for the first time in centuries. Several weeks later, Opaka Sulan was elected as the Kai of Bajor. With the destruction of the Bajoran Parliament in Ashalla and the consequent death of First Minister Li Nalas, the Vedek Assembly became the de facto government of Bajor with Kai Opaka as its leader. She used her new-found authority to have Bajor secede from the Klingon-Cardassian Alliance and turned over all of the Bajoran dissident movement's stored munitions to the Terran Rebellion aboard Terok Nor. In response, Supreme Legate Skrain Dukat sent the Cardassian Ninth Order to destroy Terok Nor and conquer Bajor. (ST - Mirror Universe novel: Rise Like Lions)