She sailed for the British East India Company carrying wheat to New South Wales for the government, before returning to Britain via China.

She spent a few years trading with the West Indies before she traveled to New South Wales again, this time transporting convicts.

[6] The Victualing Board chartered Alexander to carry 511,945 pounds (228.5 tons) of flour to New South Wales; the Bill of Lading was dated 5 March 1802.

[6][a] On 4 January 1804 Captain Norman wrote a testimonial to the Commissioners of Longitude in support of an award for Thomas Earnshaw for his chronometer.

[4] Under the command of Richard Brooks, Alexander sailed from Portsmouth on 28 January 1806, with 42 female and 15 male convicts for the colony of New South Wales.

[12] Lady Madeleine Sinclair was also carrying Captain William Bligh, who was sailing to the colony to assume the governorship.

Alexander underwent repairs at Rio after having run aground on a sand bank prior to reaching the port.