Richardson joined the club earlier in the season, making four appearances before returning at the start of 2023 to bolster Chris Willcock’s side.
In total, he made nine appearances and recorded an assist in the club’s 1-1 draw away at FC United of Manchester last month.
Hanley, meanwhile, featured 11 times for Celtic this season after joining in October.
A club statement read: "We'd like to wish both the best for the future and thank them for their efforts this season."
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