[1] As principal of the firm after his father retired from 1924 to 1955, he was responsible for many major Art Deco office buildings in capital cities in Australia and New Zealand in the 1930s, as well as many projects for the Catholic Church in Queensland, and the Great Court of the University of Queensland.

In the 1930s Hennessy designed a series large office buildings for three different insurance firms in three countries, and has been described as Australia's first international architect.

[3] Another major project was the Great Court, University of Queensland in St Lucia, Brisbane, built between 1938 and 1979.

[3] In 1950, Hennessy was awarded over £25,000 by the court when he sued to recover his unpaid fees for the Holy Name Cathedral.

[4] Hennessy died of heart disease at his eldest son's home in Sydney on 4 September 1955, at the age of 68.