Thus far, only two characters from Top Gun have been confirmed to appear in Top Gun: Maverick. Tom Cruise will obviously reprise Pete "Maverick" Mitchell and Val Kilmer will be back as Tom "Iceman" Kazansky. It's possible some other faces from the 1986 movie could be included in the sequel as a surprise, but Michael Ironside won't be one of them due to not having a good relationship with producer Jerry Bruckheimer. Ironside explained his absence thusly:
The one person still in charge is Jerry Bruckheimer and Mr. Bruckheimer and I don't really get along, or didn't get along. He offered me a project 10 or 12 years ago and ... I said no to it. The next time I saw him at a hockey game... I went up and said, 'Hey Jerry,' and he just turned around and I figured, 'Well that relationship is over with.' ... But he has a business he has to run, he has to make decisions based on his way of doing things and what makes him feel safe.
In Top Gun, Michael Ironside played Lieutenant Commander Rick "Jester" Heatherly , an instructor at the eponymous flight academy who felt that Maverick was too reckless and later "shot down" the main protagonist during a training exercise. Although more than 30 years will have passed between Top Gun and Top Gun: Maverick, Jester could certainly still be serving as a high-ranking officer in the Navy, or conversely, he's either retired or passed away. But as Ironside revealed, we won't actually see what Jester is doing nowadays.
Top Gun was one of the earlier movies that Jerry Bruckheimer produced in his career, so it makes sense that he has a hand in Top Gun: Maverick. However, Michael Ironside didn't provide any additional details on how his relationship with Bruckheimer went sour, including what project it was he turned down.
Without Jerry Bruckheimer's side of the story, we don't have the full picture, but the end result is Ironside won't appear in Top Gun: Maverick. However, maybe the sequel will have someone mention his whereabouts in passing. And as Ironside later noted in his interview with THR, he's still looking forward to seeing Maverick despite not being involved.
No official plot details about Top Gun: Maverick have been disclosed to the public yet. Among the new faces who will join Tom Cruise and Val Kilmer include Miles Teller as Bradley Bradshaw (son of the late Nick "Goose" Bradshaw), Jennifer Connelly, Glen Powell, Jon Hamm, Ed Harris, Charles Parnell, Thomasin McKenzie, Jay Ellis, Bashir Salahuddin, Danny Ramirez, Monica Barbaro and Manny Jacinto.