A winger, Frost began his career in the youth system at Second Division club Chelsea,[2] signing his first professional contract in July 1976.
[2] Frost joined newly promoted Third Division club Brentford on a one-month loan in October 1978.
[5] Frost made a name for himself on his following appearance, scoring a hat-trick in a win over Orient on 10 November and following up with another goal in a 2–1 victory over West Ham United.
Frost made his first appearance of the 1980–81 season on 3 September 1980, with a start in a 1–1 League Cup second-round second-leg draw with Cardiff City.
[2] Frost and Chelsea teammate Gary Johnson joined Brentford permanently in a £15,000 deal in December 1980.