Ms Hemstritch, along with London-based Johanna Waterous, will join the governing body as non-executive members.
The global council is responsible for the firm's overall strategic direction, its values and its governance, according to a statement from HSF.
Ms Hemstritch is a director of the Commonwealth Bank of Australia and holds non-exeuctive director roles at Lend Lease Group, Santos Ltd and Tabcorp Holdings.
She was previously managing director, Asia Pacific, for consulting, outsourcing and technology services company Accenture.
Ms Hemstritch is also a non-executive director of the Walter and Eliza Hall Institute of Medical Research, a council member of the National Library of Australia and chair of Victorian Opera.
“I’m delighted to join the Council and hope that my experience of both governance and global professional services will be helpful to the firm,” she said.
Ms Waterous, who was also appointed by HSF, is a senior independent director of RA Insurance and Reexam, as well as non-exeuctive director of WM Morrison Supermarkets and operating partner at Duke Street LLP.
She previously spent more than 20 years at consulting firm McKinsey, rising to the role of senior director.