An Eastern Suburbs junior, Allsop made it into the first grade side in 1955, in that season he was the NSWRFL leading try scorer with 18 tries scored in his 17 matches that year. In one match that year against the Parramatta Eels he scored 5 tries.
A young player from the Eastern Suburbs, Allsop made it onto the first-grade team in 1955. He was the top try scorer in the NSWRFL that season with 18 tries in his 17 matches, including a notable performance against Parramatta Eels where he scored 5 tries.