Judging by the fact that it took around a year for each of the previous seasons to be launched, the release date of Beastars season 3 could fall anywhere between April and July 2022.
It’s definitely worth checking the books out in the mean time. But if you’re an exclusive anime watcher, then you’ll have to wait for a year at least. The 3rd Beastars season is likely to have 12 episodes, judging by what we’ve seen from the previous additions.