The midfielder leaves Liverpool having been with the club since the age of six, graduated through the Academy ranks and made three senior appearances.
Clarkson debuted for the Reds as a substitute in the League Cup quarter-final against Aston Villa in December 2019 and started the FA Cup victory over Shrewsbury Town at Anfield two months later.
He then made a Champions League bow under Jürgen Klopp as he started the group-stage tie at FC Midtjylland in December 2020.
Following a temporary spell with Blackburn Rovers, the 21-year-old spent last season on loan with Scottish Premiership side Aberdeen, making 38 appearances and scoring six goals.