The 28-year-old winger heads a list of seven players not offered new deals, whilst former Huddersfield Town, Sheffield United and Bradford City striker Jon Stead has retired.
Kiernan's penultimate start for the club saw him score a hat-trick in a 5-4 win over Cambridge United. It was his 14th League Two appearance for them.
He leaves Wetherby Road along with Jake Lawlor, Melvin Minter, Jay Williams and Ed Francis, who joined as a free agent in December. Calvin Miller and Scott Brown, who have been loaned out this season, have also not been offered new deals.
Goalkeeper Joe Cracknell, who played back-up this season but was selected for this month's FA Trophy final at Wembley, has been offered a new contract.
The Trophy winners finished 17th in their debut Football League season.
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