Cowper served on the boards of 20 Australian public companies including Borg Warner Australia and Angus & Robertson.
He also held a series of appointments including President of the Law Society of New South Wales and becoming a Foundation Director of the solicitors scheme.
Together with former Prime Minister of Australia Billy Hughes, he stood for the Division of North Sydney in the 1931 Australian federal election.
He again contested the Division of Wentworth in the 1940 Australian federal election finishing behind Eric Harrison who was a sitting member and Minister.
[3] In a professional capacity he served on a series of investigations and commissions; the first Committee of Enquiry into the Salaries and Allowances of Members of the Commonwealth Parliament (1959).
Additionally, Sir Norman was a director, and frequently a chairman, of a number of public companies such as BorgWarner Australia and Angus & Robertson.
In his obituary of Cowper in the Sydney Morning Herald, Francis James described him as being "surpassed by none in his breadth and liberality of mind, integrity and undeviating, selfless care for the public interest.