Following the completion of his doctorate, Higham accepted a lectureship in archaeology at the University of Otago, and in December 1966 he moved to New Zealand with his family. In 1968, he was appointed the foundation professor of anthropology at the University of Otago. Following a visit to the University of Hawaii, he was invited by Professor W.G. Solheim II to undertake research in Thailand, and in 1969, he began his fieldwork with excavations in Roi Et and Khon Kaen Provinces. He joined Chester Gorman between 1972 and 1975 for excavations at Ban Chiang, Pang Mapha District's Banyan Valley Cave, and has subsequently excavated the sites of Ban Na Di (1981–82), Khok Phanom Di (1984–85), Nong Nor (1989–92), Ban Lum Khao (1995–96), Noen U-Loke (1999-2000), Ban Non Wat (2002-07) and Non Ban Jak (2011–17).