The notion of that there would be a trilogy of Planet of the Apes films has been around for quite some time. Matt Reeves has talked about an arc with the films, and especially with Caesar.
However, it seems the franchise might have some legs yet. Speaking too ScreenRant, both Reeves and Andy Serkis talked about the story going forward past Caesar. Reeves said:
It's all one universe and Caesar has a very important part in ape history. We think of him being the seminal figure in ape history like Moses but as the idea, that tapestry, extends outward, there are all kinds of new characters in this story that you could absolutely follow. It's really about this trajectory that all of the apes are on, that all of the characters are on, and have been very intentionally centered around Caesar, but the universe is meant to be larger than just him as well.
The way that all of the characters are drawn is so complete and nuanced, the way that Woody Harrelson's character, the way that Maurice evolves, or Rocket, all of their journeys, should you choose, you could follow the story from any point of view and it would make total emotional, psychological, and philosophical sense.
Serkis even went on to say he would consider coming back to the franchise as a completely different character, which he obviously could do, as Caesar is a digital creation. He said:
It would be an extraordinary thing to do
I really do love this franchise at the moment and I'm very eager to see where this franchise is after this arc of Caesar is done. It sounds weird to continue the films without him, but both Reeves and Serkis are right. This is a massive universe with lots of stories. I'm sure there is a good movie in it centered somewhere else.