Stan Stevens was born in Ilford and was an accomplished schoolboy footballer and cycle speedway star before coming into Speedway during the winter of 1958-59 at Rye House. Stevens' career was to take him to numerous clubs around the country, starting with Rayleigh in 1960, where he received a nomination for the title "Novice of the Year". Stan moved on to Cradley Heath in July 1961, where he won his first race and, four days later, he rode for the Heathens in a Challenge match at Yarmouth and scored a maximum. Stevens was with Cradley for two seasons, making 29 League appearances. He made appearances for New Cross (in 1963), Oxford and Southampton before joining West Ham when the track re-opened in 1964. After two seasons at Custom House, Stan moved on again, this time to King's Lynn, where he was ever-present for the Stars during the 1966 season. Stevens then returned to West Ham in 1967, remaining with the Hammers until the early 70s.

In July 1970, Stevens was a member of a party representing West Ham on a tour of Holland, where he top-scored for the Hammers in the first of two meetings against a Dutch Vikings side. As the party returned home on 14th July 1970, the minibus carrying the riders was involved in a collision involving two wood trucks and a tanker lorry, on the road between Antwerp and Ghent, near the Belgian village of Lokeren. Six occupants of the minibus were killed and Stevens was seriously injured, sustaining a triple fracture of the pelvis, a triple fracture of the left leg and serious facial injuries.

As Stevens fought back to fitness, he set his sights on a return to the saddle. West Ham looked to loan him out to a Division 2 team to help to regain his confidence and Stevens had two second-half rides on borrowed machinery after Romford's home meeting with Sunderland on 8th July 1971. An injury to Brian Foote and the transfer of Terry Shearer gave the opportunity for Stevens to join the Bombers and he made his debut at Brooklands the following week against Rayleigh, winning two races but trailing home in the other two when he failed to make the gate. Never particularly at home at Brooklands, Stan's best results came on visits to Hull and Sunderland, where he top-scored for the Bombers.

1972 saw fate take Stevens back to West Ham with the Bombers move to Custom House. Appointed captain, Stevens returned 14 points from the trip to Ellesmere Port and he scored steadily throughout the short period that the West Ham Bombers existed. Initially connected with a move to Boston when the Bombers closed, Stan ended up at Barrow, where he made 5 League appearances.