In 1872, he was appointed assistant-secretary and in 1874 secretary of Playfair's civil service inquiry commission; in this capacity he spent some time at Dublin Castle with a view to its reorganisation.

While in Ireland, Hamilton became convinced of the advisability of home rule from an administrative point of view, and he is said to have had some share in influencing both his chief, Earl Spencer, and W. E. Gladstone in the same direction.

[1] He was very much in favour of the advancement of the Australian colonies, and encouraged industrial development, and road and railway works to be undertaken during his time in office.

In 1887, he hosted an extravagant gala balls to mark Queen Victoria's golden jubilee in 1887, and was the president of the Royal Society of Tasmania.

In 1894, on Mr. Morley's nomination, he was placed on the commission appointed to inquire into the financial relations between England and Ireland, and in November of the same year he was made chairman of the board of customs.

[1] Portraits in oils by Tennyson Cole of Sir Robert and Lady Hamilton, were purchased by subscription amongst leading citizens and presented to the Tasmanian Art Gallery in 1890.

Their daughter, Anne, married Theyre à Beckett Weigall, a prominent Australian judge, and was the mother of the author Joan Lindsay.