Having previously appeared in the Football League for Rochdale, Chesterfield and Leicester, Norman Kirkman joined Exeter City as player-manager from Southampton in March 1952. Appearing just a dozen times for the Grecians he left to take up the role of manager of Bradford (Park Avenue) in March 1953. Remaining at Park Avenue for less than two years, he didn’t manage in the Football League again.   

Having played in the same Bolton schools’ team as future England international Tommy Lawton, Norman started his career as an amateur with Burnley in 1937. Signing as a professional on the outbreak of war in September 1939, he moved to Rochdale in 1946 where he finally made his Football League debut. He then switched to Chesterfield for £4,500 in December 1947 before joining Leicester City in August 1949 for an £8,500 fee. Moving to Southampton in 1950, Norman was subsequently appointed  player-manager of Exeter City in March 1952 in place of George Roughton who had taken charge of the Saints.

Norman made his Grecians' debut in a 3-0 home defeat against Northampton Town in March 1952, and played in a total of eight matches during what remained of the season as City finished in 23rd place in Division Three South.

Appearing in a further three games in 1952/53 - a season which saw the Grecians climb to 17th place - Norman left St James' Park in March 1953 to become manager of Bradford (Park Avenue) with reports of a greatly-increased salary.

Remaining with Park Avenue until January 1955, Norman didn't manage in the Football League again and combined working for a frozen food company in Sutton Coldfield with scouting for Southampton prior to a four-month stint as manager of Northwich Victoria in the mid-1960s.

Norman Kirkman died in 1995.