Trevor Parry was born in Rockhampton, Queensland, son of Dr Albert Parry and his wife, Marie (née Tornaros). His father was a Melbourne graduate and an FRCS who had left Victoria in the depression of the 1890s to set up a general practice in Rockhampton. The third of four children, Trevor matriculated from Rockhampton Grammar School at fifteen, and had to remain there a further year to reach minimum enrolment age for university. After graduation, he was a resident medical officer at Cairns Base Hospital for two years, and then did general practice locums. He returned to Rockhampton on holiday in 1928 to find his father dying. Trevor stayed to run the solo practice with its large obstetrical component, until 1939. In 1939 he married Vivienne Crank. To their disappointment it was a childless marriage, but a closely supportive one. Vivienne survived him by thirteen years.

Trevor received his commission in the Citizen Military Forces in 1930. In 1939 he commanded the 11th Field Ambulance based in Rockhampton. Soon after the outbreak of war he enlisted in the AIF, and was posted as Company Commander in the 2nd/3rd Field Ambulance, under the command of Lieutenant-Colonel KB Fraser (later Sir Kenneth). Once overseas, the ambulance was split and reinforced. Trevor was promoted to Lieutenant-Colonel and was given command of the newly formed 2/11 Field Ambulance in England in June 1940. In January 1941, the unit embarked for the Middle East. There it was involved in the siege of Tobruk, during which Trevor was mentioned in despatches. He later received the Efficiency Decoration. In 1942 he was invalided home after developing congestive heart failure. As a colonel, he took command of 112th AGH (now the Repatriation General Hospital) at Greenslopes, Brisbane, and remained there until he left the army in 1946. He then continued to hold the rank of Honorary Colonel in the AAMC reserve.

Returning to civilian life, Trevor realised that his first preference, obstetrical practice, was physically beyond him. He undertook full-time study and obtained the MRACP in May 1946. He entered private practice as a physician on Brisbane's Wickham Terrace, and was a Junior Physician at the Brisbane General (now Royal Brisbane) Hospital from 1947 to 1952. He was acting senior physician from 1952 to 1953, when he retired from the hospital due to ill health. He continued in the positions of visiting specialist physician to the Repatriation General Hospital, Greenslopes, and to the Repatriation Sanitorium, Kenmore, until 1968. He was admitted to Fellowship of the College in May 1965.

Throughout his career as a physician, Trevor's principal interests were cardiology and respiratory medicine. He was a member of the Thoracic Society of Australia. His nephew Michael Robinson, of Adelaide, is also a Fellow of the College and a cardiologist. Trevor's years in general practice engendered a strong and lasting service ethic. In his consultant years he was known for his ready availability when colleagues sought advice. His professional standing is probably best indicated by the number of his colleagues who entrusted the care of their families to him. His extra-curricular activities were limited to an extent by his poor health. Early post-war weekends were often spent surfing. Later he became a keen race-goer. He had always been interested in literature and music, and these interests predominated in his later years. Both he and his wife were particularly fond of opera.