From 2000 to 2004, Dr. Gledhill served on South Africa's National Research Foundation panels. She was President of the South African Council for Automation and Computation from 1995 to 1996. From 2000 to 2008, she served as President of the South African Association for Theoretical and Applied Mechanics and Chair of the South African National Committee for International Union of Theoretical and Applied Mechanics (IUTAM). From 2006 to 2012, she was a member of IUTAM Working Party 9 on Education and Capacity Building. She was a member of the Advisory Panel on Control Systems in Competitive Industry for National Research Foundation (NRF) and of the International Panel on Shaping the future of physics in South Africa, a process for review and foresight developed by the South African Institute of Physics (SAIP), the Department of Science and Technology (DST), and the NRF. She became President of the South African Institute of Physics in 2013.