Haynes King is not expected to miss the entire preseason. He suffered a hamstring injury during the Hall of Fame Game on August 7 and is listed as week-to-week, with an expected return within 1-2 weeks (from the Panthers page). So he'll likely miss a couple of preseason games, but he should be back before the preseason wraps up.
The Panthers did sign Kyle Trask as QB3 to cover while King recovers, but King's performance in the Hall of Fame Game (21/34, 180 yards, 2 TDs passing, plus the game-winning rushing TD) made a strong impression, so the team has every reason to get him back out there when he's healthy.