Kempson followed teammate Darren Moss to Shrewsbury Town in the summer of 2007 .His Shrewsbury début came in the 4–0 away win at Lincoln City on the opening day of the 2007–08 season. He scored his first goal for the club in the League Cup – the winner against Championship club Colchester United – three days later.
Kempson joined Shrewsbury Town with teammate Darren Moss during the summer of 2007. His professional career at the club commenced on the opening day of the 2007–08 season, when he contributed to a 4–0 victory over Lincoln City. He then scored his first goal for the team in a League Cup match against Colchester United.