Should they trust her? Hell, no. Should they ever give her any position of authority? Hell, no. Should they keep her on a tight leash? Hell, yes. But, as of right now, they have zero standing to impose actual penalty for anything. She hasn't committed any crimes in their universe.
This. Technically she’s a disposed head-of-state in exile, so diplomatic niceties and all that. They can’t lock her in the brig as she’s committed no crime. OTOH, they can’t let her run around free because, well, evil. But what they can do is listen to her. One of her titles is Dominus of Kronos. The Terrans defeated the Klingons. She knows how to fight them and beat them. Of course Starfleet being Starfleet can’t go to the extremes the Terrans did to conquer the Klingons, but the Emperor can still provide excellent tactical advise.
The biggest question remains however, what’s going to happen to her? I suspect personally, that they’ll use her presence to make the ISS Discovery stand down. At some point The Emperor will beam over to the ISS Discovery where she, Captain Killy and the rest of the Mirror Discovery crew will jump back to the MU. The Emperor having been inspired, however slightly, by the Federation will begin to take back her throne and initiate reforms which will result in Mirror Spock being able to join the Imperial Starfleet and eventually rise to become second officer of the ISS Enterprise.