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.
Allsop, a talented youngster from the Eastern Suburbs, joined the first-grade team in 1955 and excelled, leading the NSWRFL with 18 tries in his 17 matches that season. He also showcased his skills with a standout performance against Parramatta Eels.