Professor Coombes has been an academic working in Australian and US universities from 1971 to 2019. He has taught subjects in financial accounting, management accounting and corporate finance at several Australian universities, including Macquarie University, University of Technology, Sydney, the University of Southern Queensland and in the United States at Rice University (Texas) and the University of California (Berkeley).

Between 1989 and 2018, Professor Coombes was involved in senior academic leadership and management at Australian universities, including Head of School at Charles Sturt University, Dean of Commerce/Business Faculties at the University of Southern Queensland and the University of Western Sydney, and as Deputy Vice-Chancellor at the University of Western Sydney. He led or participated in many strategic projects such as amalgamations of organisations, internal organisational restructures, policy development, and enterprise bargaining.

Professor Coombes has published many articles and co-authored books.

He has presented well-received short training courses on accounting fundamentals to: Boom Logistics Limited; Brambles Limited; Brambles Industrial Services Pty Ltd; CHEP; Colonial Mutual Investment Management; Commonwealth Bank of Australia; Electric Power Transmissions Pty Ltd; Freehill, Hollingdale and Page; Transfield Services Limited.

In February 2007, the Council of the University of Western Sydney conferred the title of Emeritus Professor for his distinguished service to the University in academic leadership and to the discipline area of accounting.

Professor Coombes is a Fellow of both the Australian Institute of Chartered Accountants and CPA Australia. In 1990, he was the NSW Deputy State President of the Australian Society of Certified Practising Accountants (ASCPA) and received the ASCPA Award for Meritorious Service in 1991.