Jarrett came fourth in the 110m hurdles at the 1992 Summer Olympics in Barcelona, missing out on a bronze medal by 1000th of a second to Jack Pierce of the USA. He again narrowly missed out on an Olympic medal when he was a member of the 4 x 100m sprint relay team that also finished 4th in the Olympic final of that year. Four years earlier in 1988 he finished in 6th place in the 110m hurdles at the 1988 Summer Olympics in Seoul.
Jarrett's career was overshadowed by the achievements of fellow Briton Colin Jackson, who beat him into second place on numerous occasions at major competitions such as the World Championships, Commonwealth Games (twice), European Championships and Goodwill Games. Jackson also defeated Jarrett eight times at the national championships. In all Jarrett won two individual world silver medals and one individual bronze medal in the 110m hurdles, and another silver and bronze medal in the 4 x 100m sprint relay.