Clarke began his career with Ipswich Town as a schoolboy before signing a scholarship in 2013. He made his senior debut for the club in August 2014, before signing a professional two-year deal a month later.

He initially joined Portsmouth on a six-month loan deal in the summer of 2015, eventually making his move to Fratton Park permanent, where he became an integral part of the side.

In his first season with Pompey he helped the team reach the play-off semi-finals, and the following season was part of the team which clinched promotion to League One.

Clarke remained a mainstay in the team following that promotion, becoming Portsmouth captain, and has made 88 appearances across the last two years in League One.

He was a key member of the Portsmouth team which won the EFL Trophy at Wembley and reached the League One play-off semi-finals last season.

Shortly after joining the Albion he was sent out on loan to Championship side Derby County, going onto win the Rams Player of the Season as Phillip Cocu's side fell just short of the play-off places. 

He would return to Pride Park for a second campaign on loan the following year, this time playing an important role in keeping the Rams in the Championship.

Matt spent the 2021/22 season on loan with West Bromwich Albion, where he made 33 league appearances.