Tim Petterson left the school in July 2022 after a review of culture had found new leadership was needed.
A 96-hour civil war between the NSW Liberals and Nationals was resolved late on Monday night with negotiations brokered by former premier Dominic Perrottet.
NSW Liberal Party MPs will consider the future of the Coalition at a party room meeting on Tuesday after Nationals leader Dugald Saunders defied the opposition leader.