"Hillsborough" arrived at Madras on 13 September, and Diamond Harbour on 3 November. On her return voyage she passed Saugor on 27 December, and reached Madras on 31 January 1794. By 1 May she was at St Helena. On 20 July she reached Galway, and on 27 August she arrived at the Downs. Captain Richard Hutt left Portsmouth on 24 May 1795, bound for Madras and Bengal. "Hillsborough" arrived at Madras on 2 September and Diamond Harbour on 6 October. On 4 December she passed Saugor, reaching Madras on 7 Feb 1796 and St Helena on 7 May, and arriving at the Downs on 3 August. Hutt left Portsmouth on 18 March 1797, bound for Madras. "Hillsborough" reached the Cape on 4 June and arrived at Madras on 7 August. By 24 December she was back at the Cape. She reached St Helena on 3 February 1798 and Cork on 24 June. She arrived at the Downs on 7 July. Robert Preston and the other owners sold "Hillsborough" and she disappeared from the list of the EIC's ships. Her new owner was Daniel Bennett. Under the command of William Hingston (or Kingston), "Hillsborough" sailed from Gravesend via Portland Roads, England, on 23 December 1798, and arrived at Port Jackson on 26 July 1799. She had left with 300 male convicts, but 95 died of yellow fever and dysentery on the voyage, and six more shortly after landing. This high death toll gave rise to "Hillsborough" becoming known as the "fever ship". Governor Hunter wrote a letter to the Secretary of the Colonies:  While at Port Jackson "Hillsborough" received a new master, Captain Robert Rhodes, who had come out to New South Wales as mate on "Hillsborough". As "Hillsborough" was preparing to sail from Sydney Cove in October, a strict search found 30 stowaways aboard her. They were removed and punished. Two sailors who had aided the stowaways were also brought on shore and punished before being returned to "Hillsborough". Rhodes then sailed for the south seas fisheries to engage in whaling. "Hillsborough" spent eight months sealing and whaling around the Desolation Islands. During this period Rhodes prepared a chart of the islands, and named a bay "Hillsborough Bay". Forty years later, James Clark Ross spent some months in the islands during his expedition to the Antarctic in and .