Pieter Cloete, son of Hendrik Cloete and his wife Hester A. Lourens, accompanied Governor Hendrik Swellengrebel on a journey across the Great Fish River to present Adelaide, through the Karoo past present Graaff-Reinet, and back along the coast via Algoa Bay and Mossel Bay, from September to December 1776. He has been credited with having written the expedition's journal, but Swellengrebel himself is a much more likely author and Cloete's name on the manuscript probably indicates ownership rather than authorship. He has also been credited with compiling the neat and accurate map indicating the expedition's route, which is Map 222 of the Van de Graaff collection. However, considering his youth and inexperience he is unlikely to have contributed significantly to it and more likely it was drawm before the expedition by C.F. Brink*, with the route added later. Hence the prominence accorded to Cloete seems to have been undeserved.
After the expedition Cloete visited Europe and on his return in April 1779 was appointed as an unpaid assistant surveyor. In 1781 he was promoted to engineer extraordinary, with the rank of ensign. He married Catharina Christina Scheller on 12 September 1779.