Despite being Scottish, Handyside played his entire career in England, having initially came through the youth ranks at Heston Rovers he was scouted by Grimsby Town who signed him as a junior before promoting him to the first team in 1992.
He took his step up into the first team in 1992 and was eventually the club's long-term replacement for veteran centre back Paul Futcher and made an excellent pairing with Mark Lever.
The 1997–1998 Handyside continued to be the nucleus of Town's strong defence that helped achieve a promotion back to the First Division via the play-offs, and victory in the Football League Trophy.
After retiring from professional football Handyside worked as a delivery driver for Gilberts Furniture on the Fenton Industrial Estate in Stoke on Trent.
[7][8][9] In June 2024 it was announced that Grimsby Town and Stoke City's academy teams will play each other in annual pre-season friendlies in memory of Peter Handyside.