Q could pop up to torment the cadets on Starfleet Academy
The last we saw of Q, [John de Lancie] the eternal being who was Jean-Luc Picard's constant pain in the side, he was warning Jack Crusher [Ed Speleers] that trouble was just around the corner, so to speak. Originally, Q "died" in season two of Star Trek: Picard, but the third season brought him back to let us know that he wasn't really gone, and a new descendant of Picard's would have him to contend with. That was a perfect set-up for Star Trek: Legacy, but that hasn't happened yet.
We already know that Q can go anywhere he wants. He even popped up on Star Trek: Voyager which was stranded in the Delta Quadrant, and we already know he has no issues manipulating time as in Star Trek: The Next Generation's "Tapestry" where he shows Picard [Patrick Stewart] how different his life could have been.
All this goes to show that there is nothing stopping Q from making a trip into the 32nd century to visit Starfleet Academy. As of now, we don't know if any of the cadets will have ties to Admiral Picard or any of the other Starfleet officers Q has met. If that's the case, that would give Q even more of an incentive to show up and unleash his own brand of torment on the unsuspecting students.
We know the cadets will face a threat that will endanger the Federation and the Academy, and that dubious honor belongs to Paul Giamatti. However, that wouldn't stop Q from making an appearance as even when the Star Trek: The Next Generation crew had other villains to contend with, Q would still make an occasional drop-in just to stir things up.
We also know that Q can change his appearance so de-aging would not be required for de Lancie's character to create havoc at the school, and quite frankly, with what the cadets will be facicng, there should be some moments of levity like the ones Q can bring. Who doesn't remember Worf's aggrieved "Sir, I protest. I am not a merry man!"