I have just started employment as a New Graduate registered nurse in the public health system. 
As I have no prior public service, when can I access paid sick leave?

In short, not immediately.  Under clause 37(i) of the Public Health System Nurses’ and Midwives’ (State) Award 2015, an employee is not entitled to paid sick leave until after three months continuous service. 

The relevant Ministry of Health policy directive (PD2024_046 Leave Matters for the NSW Health Service) also states that “After the first three months of service Employees become eligible for a full year’s entitlement of paid sick leave on the first day of the fourth month of employment.” 

Therefore, paid sick leave becomes initially available after the completion of the first three months of service and subsequently then on your anniversary day.