Dr Leung began his career in public health and administrative medicine in 1985. He was appointed Deputy Director of Food and Environmental Hygiene in 2000 and Deputy Director of Health in 2002 in the Department of Health of the Hong Kong SAR Government. He set up and became the first Controller of Centre for Health Protection in 2004. As Controller, he was responsible for disease prevention and control as well as public health emergency (including major infectious disease outbreaks and pandemics) planning and response in Hong Kong.

Dr Leung joined the Hong Kong Hospital Authority as Director of Quality and Safety in 2007 to lead, plan and launch initiatives to enhance quality, patient safety and risk management. He was appointed Chief Executive of the Hospital Authority in 2010 and retired in August 2019. He was responsible for the overall management of 43 public hospitals and other healthcare institutions, about 80,000 staff and an annual operating expenditure of over HK$70 billion.

Dr Leung is currently the Honorary Clinical Professor in the School of Public Health of the University of Hong Kong, and Honorary Professor in the Department of Medicine and Therapeutics of The Chinese University of Hong Kong.