One of several players from South Wales who arrived at St James' Park around the same time, Norman joined the Grecians on part-time forms when leaving the Army on completion of his National Service in July 1955. He combined playing for the club with his teaching career which took him to working at Exmouth Grammar School where he taught English and French. 

A regular in City’s reserve team throughout the 1955/56 season, playing 35 times in the Southern League, Norman was called up into the first team to make his debut at Crystal Palace in January 1957. He went on to make seven appearances for City’s first team that season, and started the 1957/58 season playing in the opening fixture at home to Southend United. 

He was in and out of the side throughout 1957/58 and was torn between becoming a full time professional or continuing to combine football and teaching. City manager Norman Dodgin urged caution and Norman remained part-time. Eventually enjoying a total of 18 league outings, he mainly appeared for the reserves in both the Southern and Western leagues as an understudy to the dependable Keith Harvey.

After leaving St James’ Park at the end of the 1960-61 season, Norman signed for Western League Bridgwater Town where he enjoyed several good seasons before retiring from playing. His connection with Exeter City was far from over for, after retiring from the teaching profession, he worked for Greenslades coach company and ended up becoming  City’s coach driver on away trips.

Norman, who continued to live in Exmouth, died on 25 September 2009.