Clarke, 21, joined the Reds in August 2019 from Bradford Park Avenue.
Bowman, 28, also joined the club in 2019 and has impressed in his time so far.
Hebson, 23, is in his second spell at the club and has been a regular in the first-team squad since returning to Borough Park in 2019.
On the re-signings, manager Danny Grainger said: "Clarkey is another young player who we think there's more to come from.
"I'd like to see him get more assists and goals as he's a fantastic player, and a great lad to have in the squad and around the dressing rooms.
"Chaz is a player who I can't speak highly enough of; he's a fantastic lad to have in the dressing room, he never lets us down when called upon and he's got a great relationship with the fans.
"Robbie was very unlucky with his injury last year, we still think there's loads to come from him and he's just going to get better and better."