After a successful career at Cherry Orchard in 1997 Dempsey signed a 4-year contract with Everton and moved to Merseyside soon after his 16th birthday.
He spent 4 years at Everton and was part of the team that won the FA Youth Cup with the likes of Richard Dunne and Francis Jeffers.
[5] Dempsey struggled to hold a place in the Aberdeen first team and he spent time on trial with Doncaster Rovers in January 2006.
On 26 March 2007, Aberdeen announced that he had rejected their final contract offer,[6] and shortly afterwards he signed for Yeovil Town.
He started the league campaign with a 6–0 loss against South-East rivals Wexford Youths, then went on to beat hot favourites for the title Limerick 3–1.