Yes, there will be another Star Trek movie. J.J. Abrams' interpretation of Star Trek will continue to explore strange new worlds, however, it will be doing so without Chekov. It looks as though Abrams plans to drop the character after the untimely death of Anton Yelchin.
Well, I guess in this alternate timeline anything is possible.
I hope that the conclusion of the Chekov story will be handled tastefully. Before killing the character off, I might remind Abrams that another actor made the role famous.
By the way, Chris Hemsworth will appear again as George Kirk in Star Trek 4. Really? Why? My thought, Hemsworth sells tickets.