Later career (1883–1895)
Robinson served as the governor of South Australia, beginning in February 1883; the song "Unfurl the Flag", which he had composed, was played during his inauguration in Adelaide. Due to few important political events occurring in the late 1880s and the fact much of the political power was within the Premier and the legislative assembly, Robinson had little to do as governor, making his role primarily needed solely for symbolic and social purposes.
Robinson was passionate about music, playing the violin, piano, and singing. Throughout his time as governor of South Australia, he was involved with music-related groups. Robinson organised the Adelaide Jubilee International Exhibition in 1887 and was largely responsible for instituting the Bachelor of Music course at the University of Adelaide. He had composed multiple songs previously in his life, including "Imperfectus", "I love thee so", "Remember me no more", "Severed", and "Thou art my Soul", which by this point had become well known in Australia. Robinson also composed a whole comic opera, which was presented at the Princess Theatre in Melbourne, Victoria. Performing in a variety of different events throughout the 1880s, he entertained the most people at Government House of any Australian governor.
In addition to composing music, Robinson was a part of literary and educational groups in Australia. The Physical Geography of the South-West of Western Australia, a paper he wrote and had published in 1886, was read to the Royal Geographical Society of Australasia, as well as On Duty in Many Lands, which was published in 1884. Robinson was also a public speaker. He departed from Adelaide in 1889.
Robinson was promoted to Knight Grand Cross of the Order of St Michael and St George (GCMG) on 24 May 1887. Also in 1887, he turned down a request for his governorship of Hong Kong, as he did not want to undergo its harsh climate. During 1889, from 9 March to November, while Henry Brougham Loch was away, he acted as governor of Victoria, Australia, but was never officially appointed to the position permanently. Due to Robinson's success as temporary governor, the Leader of the Opposition and the Premier were planning to request for Robinson to become the next governor once Loch's governorship concluded, but Lord Hopetoun was appointed before they got the chance. A new divergence had been taken up by the British Government, giving highly ranked positions in the government to noblemen who were inexperienced, which annoyed Robinson. Shortly afterwards, Robinson rejected the governorship of Mauritius.
After his temporary governorship of Victoria, Robinson travelled to London, England. There he assisted the delegation of Western Australia and the Colonial Office by helping pass the constitution bill through parliament. In September 1890, he went to Perth, Western Australia. Robinson became the governor of Western Australia for a third time in October 1890; his return was praised enthusiastically by the citizens. According to the Australian Dictionary of National Biography, "he knew and understood more about Western Australia than any other imperial officer." Robinson chose John Forrest to be the first Premier of Western Australia. Robinson had little to do involving politics as governor, due to the fact that Forrest was dominant over the cabinet and parliament, as well as because of constitutional conventions. His time as governor included the transition of the colony to self-governance in 1890. Robinson was offered the position of the colony's first agent general by Forrest 1891; however, he declined the offer.