In September 2015 Professor Brady took up the position of President and Vice-Chancellor of the University of Bristol- a member of the UK's Russell Group of elite research-intensive universities. Professor Brady is President Emeritus of University College Dublin (UCD), where he served as President from 2004 until the end of 2013. During his tenure Professor Brady oversaw a major institution-wide transformation programme that included expansion of UCD’s science, engineering and biomedical research capacity, through the development of the O'Brien Centre for Science, Conway Institute for Biomedical Research, UCD Clinical Research Centre, the Dublin Academic Medical Centre and the Ireland East Hospital Group.

In addition, he led a major growth in UCD’s international footprint. A nephrologist by training, Professor Brady was Professor of Medicine and Therapeutics at UCD before being appointed the university’s President. Prior to that, he built a successful career as a physician and biomedical research scientist in the US, spending almost a decade at Harvard University, where he was Associate Professor of Medicine, Director of the Renal Division of the Brockton/West Roxbury VA Medical Center and Consultant Physician at the Brigham and Women’s Hospital, Boston. He has an international reputation in the pathogenesis of diabetic kidney disease and renal inflammation.