Stuart is a graduate  the University of Glasgow in 1980 and was admitted as a solicitor in Scotland in 1982. After completing postgraduate studies in oil and gas law at the University of Dundee he worked in private practice, specialising in corporate law and intellectual property and was a partner in a Glasgow based law firm until 1994 when he started his academic career at Dundee Law School. He retired from Dundee in 2019 and is now Emeritus Professor of Law.

He has extensive experience of charity law and governance and has been a trustee and chair of many arts and culture focused charities including Dundee Contemporary Arts, Fife Cultural Trust, Hospitalfield Trust and Leisure and Culture Dundee. He was a board member of OSCR, the Scottish Charity Regulator, and is currently a trustee of the Royal Conservatoire of Scotland. He is the co-author of two of the leading texts on charity law in Scotland and is a Writer to the Signet. He is a Fellow of the Higher Education Academy and a Fellow of the Royal Society of Arts.​