Graeme acts extensively for healthcare professionals, particularly doctors and dentists. He represents professionals in clinical negligence claims and before the regulators, including the Medical Practitioners Tribunal Service and the General Dental Council. His practice covers fatal accident inquiries and public inquiries. He undertakes judicial reviews arising from healthcare disputes. He is ranked band 1 in Chambers & Partners and tier 1 in the Legal 500.

His disciplinary and regulatory practice extends to teachers, actuaries, accountants and other professions. He sits as a legal adviser to the disciplinary tribunal panels of the Institute and Faculty of Actuaries.

Graeme also has a disease litigation practice with particular emphasis on historic abuse. He has given evidence to the Scottish Parliament on historic abuse and represents key core participants in the Scottish Child Abuse Inquiry.