The teenage midfielder has impressed for the club's development squad this season, earning a place as an unused substitute in the recent home game against Cheltenham.
Hare has also accompanied the first-team squad on away trips, and has caught the eye of his manager Martin Allen.
Allen told the club's official website: "Josh has been outstanding in the last two development games in the holding central midfield role.
"This boy is very well-behaved, conscientious and caring and a pleasure to work with.
"He listens, he learns and is a sponge for information. The last rung of this ladder is the hardest to climb and requires a commitment to get bigger, stronger, faster and more powerful and to be a good athlete."