The NHMRC Clinical Trials Centre at the University of Sydney has multiple positions available for biostatisticians. Positions are available for qualified individuals at both entry level and experienced level. If you are interested please see the job postings on the university's career site:

entry level link: 

https://usyd.wd3.myworkdayjobs.com/USYD_EXTERNAL_CAREER_SITE/job/Camperdown-Campus/Biostatistician_0100372-3

experienced level link:

https://usyd.wd3.myworkdayjobs.com/USYD_EXTERNAL_CAREER_SITE/job/Camperdown-Campus/Biostatistician_0100381-2

Applications close 3 Feb 2023. Note that visa sponsorship is not available for these positions so applicants will need to have the right to work in Australia.