The Galactic Council are the the highest ranking authority of the Galactic Guardians. Their actual position in the Guardian hierarchy is unknown, though they seem to be high up. They function as a deciding body and court system for the Guardians.
When what appeared to be Atomic Betty caused havoc in the Interstellar Diner, the Galactic Council became up in arms, with practically every law-enforcement agency in the known universe was sent to look for Betty. (The Trouble with Triplets)
Boltar framed Admiral DeGill for lying about a victory in battle and had him brought before the council for trial. Boltar had temporarily managed to get DeGill arrested and assumed the position as Vice-Admiral, but fortunately, Betty and her team found Arkan, a former Galactic Guardian who witnessed the battle, and proved DeGill's innocence. (License DeGill)
After X-5 completed a Time Machine, Admiral DeGill was ordered to present the time machine to the Galactic Council. However, this was a trap set by Maximus, who disguised himself and Minimus as the council and managed to capture the time machine. (The Future Is Now!)