Anybody appointed to a leadership role by the Sydney Archdiocese of the Anglican Church would have been chosen on religious grounds first with other qualifications being secondary. The archdiocese controls the councils of all of these schools (including Shore) and is heavily dominated by evangelical christians. Non GPS/CAS Anglican schools in Sydney go further and even require teachers to be a member of an evangelical church to get a job.
Tony George at Kings is the son of an Anglican minister.
Tim Bowden at Trinity is an ordained Anglican minister
John Collier at St Andrew's is a member of Chapter of St Andrew’s Cathedral and Lay Canon of the Cathedral
You'll note that in the link provided Dr Pettersen didn't use the words academic or sport once in his welcome to the school.
https://www.spcc.nsw.edu.au/port-stephens/our-story/meet-the-school-principal
I remember the good old days of true Anglican educators. People like..
1. Rev Kurrle at Kings
2. Rod West at Trinity
3. Canon Newth at St Andrew's
4. Basil Travers at Shore
Those days the school direction was not dictated by the evangelical edicts of the Diocese of Sydney.