Clarke’s contract expired at the end of the season, and his departure brings to an end his three years at The Shay.
The 37-year-old joined his hometown club from Grimsby in the summer of 2018 and completed his 20th season as a professional in the 2020-21 campaign.
He made more than 100 league appearances for The Shaymen, and took over as skipper from Matty Brown at the start of last season, missing part of the campaign through a career-threatening eye injury.
He joins Danny Williams, Reuben Noble-Lazarus, Jack Earing and Jeff King in leaving the club so far this summer.