The character often had more fleeting interactions with other characters of the crew on Star Trek: The Next Generation, with the meat of his appearances tied to Patrick Stewart’s captain.
I’d love to see what Q could do to mess with Rios and what further details about the character could surface in the process.
It seems that could also happen in Star Trek: Picard Season 2.
Based on that answer, it’s possible that Q’s main storyline solely involves Jean-Luc Picard, which would be in line with a lot of his past appearances.