Hmmm.... well if we go by 'patterns'. The recent one starting in XY with the Water Starter, Fire Bird, and no Grass Type, followed in SM by the Fire Stater, Grass Bird (also Starter), and Water Type.
This suggests Ash won't be getting a Fire type at all this time, but he will be getting at least the Grass Starter (Grookey), the Water Bird (Cramorant or something else*), maybe the Water Starter (Sobble, he's done 2 water types on the team before), and the pseudo legendary. Counting Larvitar's honorary status he's done one every even number generation. So I'll bet good odds on him getting one in the eighth.
*Galar Fearow (Water/Flying)
So at the very least he'll get 4 Galar Pokemon, I'm sure he'll get a fifth one, but it'll be the wild card so no clue what'll be.
As he goes through the other regions I'd love to see him pick up or at least meet his old pokemon: Goodra, Greninja, Butterfree, Primeape, Pidgeot, Lapras, Larvitar, etc.
As for catching new pokemon?
Dear Writers,
Please just give Ash a Lucario already when he's in Sinnoh would you?
Thanks,
The Fanbase.
(You know people are going to bring this up eventually)
Ash's team should be no bigger then 12 imo Pikachu + 11 others. That's two teams: a main one and a reserve one.
I just remembered: Larvitar appeared in a flashback during the Kanto Two Partner! I don't know if that means anything, but at the very least it means the anime staff hasn't forgotten him! Maybe we will see him again when Ash travels to Johto?