The 23-year-old centre-back joins forward pair Carl Stewart and Carl Ansu as manager Chris Bolder's latest recruits.
Clappison was released by York City last month having managed only nine starts following his arrival from Hull City in May 2016.
He went on to agree a deal with Alfreton just over a week ago, and made his debut in their 3-1 home defeat to Bradford Park Avenue last Saturday.
Stewart is a former Ossett Town, Frickley Athletic and Bridlington Town frontman who went on to finish the season with 19 league goals for Tadcaster Albion last season.
He re-joined Scarborough Athletic for a second spell at the start of this season after being with Shaw Lane AFC, and has more recently been with Goole AFC.
Ansu returns to Ferriby, where he came through the club's academy system, after spells with Hull United and Hall Road Rangers.