Adam signed for the Bantams in January 2022 on a short-term contract until the end of 2022/23 season.
The experienced midfielder started his career at Manchester City aged seven, and, under City chief Mark Hughes, signed his first professional contract with the club in May 2007.
The 34-year-old found regular first-team football at Leeds United where he netted six times in 45 appearances, before attracting a successful move to Huddersfield Town.
Seven goals in 42 apperances at the John’s Smith Stadium saw £1.5 million a move to Middlesbrough, where in his first season at Riverside, he won promotion to the Premier League.
Spells at Birmingham City and Doncaster Rovers ensued, before making a move to the University of Bradford Stadium.
Clayton featured four times for England at under-20 level.