Her role as the Principal Consultant, Ethico-Legal Reform for the South Australian Government entailed developing, reviewing and proposing amendments to policy and legislation at State and Commonwealth levels in ethically complex areas. Dr Murray has represented the SA government on national Health Ministers’ policy advisory groups in areas such as genetics, privacy, autopsies, organ donation, assisted reproductive technology, surrogacy, human cloning and embryo research. She has served as a Director on state and national health, bioethics and education boards, has presented at bioethics conferences and is an active member of state and national bioethics organisations. She is the Secretary of the Australasian Association of Bioethics and Health Law.
Dr Murray is active in women's policy at state, national and international levels, having served on the South Australian Women's Advisory Council and one of the Commonwealth’s Women's Secretariats, and as a Trustee on the SA Women's Trust. She has served at national and international levels as a Director on the Executive of BPW (Business and Professional Women), a supportive network which advocates for business and professional women at the United Nations and to national governments, and has presented workshops around the world on organisational management and governance.