Eldryd Parry studied medicine at Cambridge and Cardiff and was seconded from 1960 to 1963 to University College Hospital, Ibadan, Nigeria. In January 1966 he returned to Africa at Haile Sellassie I University, Addis Ababa, and left in 1969 to take the Chair of Medicine at Ahmadu Bello University, Zaria, Nigeria. In 1977 he became the Foundation Dean of Medicine at the University of Ilorin, Nigeria, , where he introduced a radical community based programme, COBES. From 1980 to 1985 he was Dean and Professor of Medicine at the now Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.
He was senior editor of Principles of Medicine in Africa until 2009 (4th Edition, Jan 2013). He was an Honorary Fellow at Cardiff, Emmanuel College Cambridge, the London School of Hygiene and Tropical Medicine, the Royal College of Surgeons of England, the College of Physicians and Surgeons of Ghana, and a Foundation Member of the Faculty of Medicine and Surgery of Amoud University, Somaliland. In 1988 he founded THET, which he chaired until 2007. He was given a lifetime achievement award by the Royal Society of Tropical Medicine and Hygiene in 2007. He received the OBE in 1982 and was appointed KCMG in 2011.