Hocking was born in Caerleon, near Newport, Monmouthshire in south east Wales but was raised in Rhodesia, now known as Zimbabwe. As a teenager, he began racing motorcycles on grass tracks. Before long, he had moved on to road racing circuits.
He left Rhodesia to compete in Europe in 1958 and made an immediate impact, finishing 3rd behind the works MV Agustas at the Nürburgring. He was sponsored by Manchester tuner/dealer Reg Dearden, who provided him with new 350cc & 500cc Manx Norton racers. He spent the winter of 58/59 with the Costain family at there home "Lindors" in Castletown on the South of the Isle of Man, learning the Isle of Man TT course with George Costain, an established rider for the Dearden team, who had won the Senior Manx Grand Prix on a 500 Dearden-tuned Manx in 1954. In the 1959 Junior TT, he finished an amazing 10th from 22nd on the grid, a fantastic achievement for a first-timer to the circut. In 1959, he was offered a ride by the East German MZ factory and finished second in the 250cc championship. During practice for the 1959 Junior TT, his & the machines of fellow team mates Terry Shepherd & John Hartle 350 Manx's were fitted with the top-secret works 350cc Desmodromic engine, but they ran standard engines for the actual race. George Costain was offered one of the practice engines for the race, but declined the offer as this was to be his last Junior TT before retiring & he wanted to be sure of going out with a finish, rather than risk a retirement with a blown engine MV Agusta offered Gary full factory support for the 1960 season and he repaid their confidence by finishing 2nd in the 125cc, 250cc and 350cc classes.
Following the retirement from motorcycle racing by defending champion, John Surtees in 1961, Hocking became MV Agusta's top rider and went on to claim dual World Championships in the 350cc and 500cc classes, dominating the season completely.
Hocking was affected deeply by the death of his friend, Tom Phillis at the 1962 Isle of Man TT. After winning the Senior TT, he announced his retirement from motorcycle racing and returned to Rhodesia. He felt motorcycle racing was too dangerous and decided a career in auto racing would be safer.
Ironically, later that year he was killed during practice for the 1962 South African Grand Prix at East London South Africa. His car, a Lotus 24, went straight on a fast curve and somersaulted after hitting a ditch. There is speculation that he blacked out on the long back straight as he made no attempt to slow down or steer into the corner as the car carried on into the bank at full speed. He was 25 years old.