Before the release of Star Trek Beyond, there have already been talks to bring forth Star Trek 4. The most recent news is an idea that was pitched. It involved Chris Hemsworth returning as George Kirk. Chris Hemsworth heard the idea and he praised it. This means that the next Star Trek may deal with time travel. From what it sounds like, the film would involve James and George Kirk working together as father and son to stop a threat. The only thing that remains to be seen is the execution of that plot. From what it sounds like, this could be the last of the Star Trek reboot movies.
Star Trek was off to a strong start with the 2009 reboot. Then they worked on recreating The Wrath of Khan with Star Trek: Into Darkness. The interesting thing is that The Khan story is a recurring plot throughout the Star Trek film franchise. It has occurred with First Contact,Nemesis, and Star Trek as well. Beyond has taken a different direction with elements from The Search For Spock. It looks like Star Trek 4 is borrowing heavily from The Voyage Home, except the plot is going to be entirely different other than time travel.
It might take a lot of effort to screw this effort up. However, Star Trek Beyond is considered to be a better film than Into Darkness. The only issue is that they are going to have to wait a bit before they can get the project off the ground. For one thing, some of the cast members are committed to other upcoming movies. Chris Hemsworth and Zoe Sadana are in Avengers: Infinity War and Guardians of the Galaxy respectively.