Shaw was educated at Melbourne Grammar School, where he was on the debating team, played violin in the orchestra and was awarded the Frank Grey Smith Scholarship for Classics or Modern Languages.

From 1941, alongside these government positions, Shaw returned to Melbourne University as part-time lecturer in economic history and tutor at Trinity College.

[citation needed] In 1950 he was awarded a Nuffield Dominion Travelling Fellowship and spent a year undertaking research in England into Australia's convict period.

[10] In the early 1960s Shaw was called upon to adjudicate on the long-running Australian TV quiz show Pick A Box when contestant Barry Jones disputed the answer given to the question "Who was the first British Governor-General of India?".

Shaw returned to an academic position in Melbourne in 1964 as professor of modern history at Monash University, only three years after teaching commenced there.

A review of his History of the Port Phillip District (1996) thought it a "meticulously researched and carefully crafted work which Shaw's earlier writings have led us to expect.

[13] In 1987 Shaw was elected president of the Royal Historical Society of Victoria, and also served as a member of their finance, fellowship, speakers and editorial committees.

[23] In 2002, having sat on the editorial board from its formation in 1960 until 1999, as well as being section editor for the first two volumes and contributing ten articles, he was awarded the inaugural Medal of the Australian Dictionary of Biography.