He had been a member of the diplomatic service before entering politics and later served as High Commissioner of Australia to South Africa from 1998 to 2002.

In 1974 Connolly was selected as the Liberal candidate for the very safe seat of Bradfield on the retirement of the then member, Harry Turner.

He was elected to the Australian House of Representatives, and held the seat until 1996, when he was defeated for preselection by future Liberal leader Brendan Nelson.

[1] Before serving as Australia's High Commissioner to South Africa between 1998 and 2002 with accreditation to Botswana, Lesotho and Swaziland, he was appointed an adviser to the first multi-ethnic South African Parliament by the Commonwealth Secretariat, Connolly later developed a close relationship with Nelson Mandela and accompanied him to Australia as a guest of the Howard government.

[4] In June 2022 he published Sunshine and Shade, a memoir of his childhood in Sri Lanka and his political and diplomatic life.