He may return later in the series though.
Icon Comics is a subsidiary of Marvel Comics. It was created as a publisher that focuses on creator content, allowing Marvel's writers to release their own original stories without having to leave the company. Kick-Ass and Kingsman are two comics from Icon that made it to the big screen. 21st Century Fox was behind the Kingsman franchise, but the Disney merger has placed the film back under Marvel's umbrella. Kingsman 3 is slated to hit theaters in 2019, but the film's main actor won't be a part of it.
Taron Egerton blew up off the success of the Kingsman franchise, but in a recent interview, he revealed that he won't be in the third film. Speaking with Yahoo!, Egerton stated, “I don’t know how hot off the press this is, and I think I’m allowed to say it, but I’m not in the next Kingsman movie." Although that may discourage fans of the film, he continued on to hint at returning for another movie in the franchise. “That doesn’t mean I won’t be in Kingsman ever again. I was with Matthew [Vaughn] as little as a few days ago, we’re still very much in business together, but his next journey in that world doesn’t involve me.”