At this time, the focus of political power in the Imperium was the ruling monarch (Imperial Sovereign) and the Shi'ar-dominated Imperial Council. The Assembly of Alien Races did not exist at this time.
By Year 6500, the New Shi'ar Imperium controlled almost all of the Pocket Universe, at least nominally.
It was during this time that non-Shi'ar races within the Pocket Universe gained Hyperdrive technology for the first time.
Chandilar at this time was de facto universal capital of the Pocket Universe.