Lady Penrhyn, William Sever, master, left Portsmouth on 13 May 1787, and arrived at Port Jackson, Sydney, Australia, on 26 January 1788.

She was part of a convoy of eleven ships, the First Fleet, which brought over 1000 convicts, marines, and seamen to establish European settlement in Australia.

Bowes Smyth then took charge of the prisoners on the ship when Altree fell ill at Tenerife and in Governor Arthur Phillip's opinion had proved unequal to the task.

[9] The list of stores unloaded from Lady Penrhyn on 25 March at Port Jackson has been widely quoted in books on the First Fleet.

[12] Having discharged her convicts in New South Wales, Lady Penrhyn then was under contract to George Mackenzie McCaulay, an alderman of the City of London, to go to the "North West Coast of America to Trade for furrs & after that to proceed to China & barter the Furrs &ca for Teas or other such Goods..."[13] Her owners had obtained a license to sail to the northwest coast from the South Sea Company, which still maintained its ancient monopoly rights over British trade to the eastern Pacific.

Sever then sailed to and named Penrhyn Island—the atoll of Tongareva in the Cook Islands—on 8 August, arriving at Macao on 19 October 1788, and proceeding upriver to Canton (now Guangzhou) to take on a cargo of tea.

[19] On 22 July 1811 the French privateer Duc de Dantzig captured Lady Penrhyn while she was sailing from London to Grenada.