I've never run one, but now I want to!
I'd imagine that there are faerie versions of magi, maybe the founders, discussing both old and recent topics. I mean, each magus has an opinion about what "the Tremere" will do. The fae reflect this expectation, so you have a faerie in the likeness of Tremere the founder, who has the opinions not of house Tremere, but of what the collective of 1000 magi think is the opinion of house Tremere (which might be quite different).
Maybe there are a few cases reflecting the current state of the order, and someone attending could predict the probable outcome of the Tribunal. Example:
The next Grand Tribunal will discuss the creation of a Lotharingian Tribunal, and a magus decides to attend the fae Grand Tribunal that will happen two years before. After some discussion the creation of the new Tribunal is rejected, but the magus realizes that the fae with a wolf head had doubts, and if he had voted differently it would have swayed the others opinions and the motion would pass. There was also some turmoil because a french lion that was staunchly against Lotharingia was killed by his son during the Tribunal.
Assuming that the faerie Tribunal mirrors what will happen on the Grand Tribunal, the Lotharingian movement will lose, but this can be changed. The wolf faerie represents a specific Tribunal, maybe Rome? A house, maybe the Tremere? Or a specific person, someone with a wolf familiar, or maybe a wolf heartbeast? Can his position be changed?
The lions probably come Normandy. Is this betrayal between a covenant and it's vassal? Or is there a real murder about to happen?
This ended up as a story seed kind of thing, which wasn't quite my intention... But anyway, I'd expect this kind of thing, coupled with petty arguing between the faeries (because magi are petty).
The faeries can be as literal or as figurative as you want. Maybe they aren't animals, but people, and the attending magus needs to talk to them to discover who is who (but I'd expect some to represent covenants, some to represent Houses, some to represent actual persons that are sure to show up in the hermetic Grand Tribunal).