He was the first Cook Islands medical graduate in New Zealand, finishing his studies at the University of Otago in 1945. He then served as Medical Officer in the Cook Islands working to improve the country's health system.
In 1952, he went to Harvard University, initially completing a Master of Public Health, before joining their Department of Nutrition. Subsequently, he worked for various parts of the armed forces as a research physiologist, before joining NASA to work on the space program.
Davis was a founder of the Cook Islands Democratic Party in 1971, and became opposition leader in 1972, going on to serve as Prime Minister from July 25, 1978 until April 13, 1983, and following the short first tenure of Geoffrey Henry, again from November 16, 1983 until July 29, 1987, when he left office while the Democratic Party was still in power.
On August 3, 1986 Davis became the first head of government to formally consult with the Universal House of Justice.
He later went on to serve as High Commissioner to New Zealand.