Gym Leaders:
Brock, Misty, Erika, Janine, and Sabrina would definitely stick around, given how they're still relatively young. Another Trainer might even take Blue's place, as he may either stay and monitor the Battle Tree with Red or even spend time with Oak in his apparent final years.
Lt. Surge might move some ranks, and, as one user put it very well, could even become an Elite Four member. I personally see him either becoming a professional sports coach or even returning to the army, though.
Blaine would definitely retire. I'd imagine a very energetic and scientific young woman taking his place, just to keep Cinnibar and the Seafoam Islands as lively as ever.
Elite Four:
Lt. Surge could hypothetically take Bruno's place. I'd imagine Bruno himself may even step down and train in Mt. Silver, especially when Red is no longer there, given his prestigious position in Alola.
The Pokémon in Mt. Silver are more than perfectly strong enough to keep Bruno and his Pokémon in shape. He might even take the Karate King's unsuccessful and youthful apprentices under his wing.
I would imagine that Agatha might be dead by now, while Lorelei makes it her mission to keep both the Sevii Islands and Kanto safe. I'd hope the former makes peace and gets positive personal closure on her history with Oak beforehand.
Lance is still the Champion, all things considered. His role in helping Ethan, Kris or Lyra take down Team Rocket is a feat worthy of maintaining the highest possible authority a strong trainer like himself might have for life.
Will and Koga would definitely still be around. Karen may even become a mom. I'd imagine she would have a daughter who eventually takes her place.
The Region itself
The place becomes much cleaner, as Erika's efforts for a greener and more environmentally friendly Kanto would be accepted and executed by many.