Prof. Rapper has held several academic and non-academic appointments in Australia, the United States and the UK as the Dean of Engineering at the University of Sydney, Head of Chemical & Biological Engineering at University of Missouri in United States, Division Director of Chemical, Bioengineering, Environmental Engineering and Transport Systems at the National Science Foundation in United States and Deputy Vice-Chancellor (Research & Innovation) at the University of Wollongong. Her last appointment was Dean and Chief Executive Officer of TEDI- London responsible for the development of a new start-up Engineering Institution (from 2019 to 2023).