Connor was born in Wollongong, New South Wales. He served on the Wollongong City Council from 1938 to 1945, and then in the New South Wales Legislative Assembly from 1950 to 1963. After entering federal politics, Connor became an ally of Gough Whitlam, who appointed him to cabinet when Labor won the 1972 election. As Minister for Minerals and Energy, he was noted for his strident economic nationalism. However, Connor is best known as the central figure in the "loans affair", which arose from his attempts to secure petrodollar loans from Middle Eastern financiers. His resignation from cabinet in October 1975 precipitated the constitutional crisis which resulted in Whitlam's dismissal a month later.