Career
Gitsham began his career in the youth team at Division Three side Brentford. At age 18, while still a part-time player, Gitsham made his professional debut in a 2-2 draw with Hull City at Griffin Park on 8 April 1961. He went on to establish himself in the left back position, but lost his place in the team to new signing Allan Jones.
Gitsham made 61 appearances before departing the Bees in the summer of 1963.
He later played non-league football for Romford and Stevenage Town and was forced to retire due to a broken ankle.