Dr Graham attended the University of Newcastle for his medical degree and worked as an intern and resident medical officer at Westmead Hospital in Sydney. He was awarded Junior Medical Officer of the Year. Desmond trained as a Geriatrician at Westmead Hospital and Royal North Shore Hospital in Sydney from 2015-2020. During this time he was awarded Senior Registrar of the Year and Registrar Excellence in Teaching. He gained his fellowship of the Royal Australasian College of Physicians (RACP) in 2020 and immediately started working as a Visiting Medical Officer at Northern Beaches Hospital.
At the same time he joined the private consultant centre Brellah Medical Practice in Frenchs Forest. Alongside his private and public work, Desmond has been heavily involved with teaching and curriculum development for the medical school at the University of Sydney. He holds the title of Clinical Associate Lecturer. Desmond is an active member of the Australian and New Zealand Society for Geriatric Medicine. He is part of the Policy & Planning and Geriatric Medical Education & Training committees.