Three council members stepped down from the council last week, and school council chair Robert Utter warned that if there were any more sudden resignations, Trinity Grammar would have to enter into administration.

In a video address to parents and staff, Mr Utter said the school had brought attention to itself for all the wrong reasons.

"This is extremely unfortunate and disappointing," he said.

"It saddens me to say that never in my 30-plus years as a Trinity parent and school council servant have I observed the sort of behaviours we have seen in the past two weeks; behaviour that has only served to bring the proud name and heritage of Trinity Grammar into disrepute."

He urged everyone to "take a breath, find calm and act with respect".

The school plunged into an administrative crisis two weeks ago after popular deputy principal Rohan Brown was sacked for cutting a boy's hair.

The decision to sack Mr Brown sparked chaotic scenes at Trinity Grammar, where students staged protests, chants and ditched their school uniforms to show their support for Mr Brown.

At a heated community meeting, more than a thousand parents, students and alumni voted for the school council and principal to stand down, saying they had lost confidence in the school leadership.

Mr Utter said council members would continue to govern the school and, in time, stand down. They will then be replaced.

There are concerns that the vocal campaign to reinstate Mr Brown went too far this week when disgruntled parents funded a truck that circled the school with electronic billboards criticising the principal and council.

Some parents have accused their peers of bullying principal Dr Michael Davies, and said the truck was indulgent, embarrassing and over the top.

Mr Utter said the council was very close to falling below the constitutional quorum that allows it to operate.

Any further resignations would mean that the school would have "no choice" but to enter into administration, with a court appointing a new administrator, he said.

"School council is of the view that administration would have negative consequences for the school and should be avoided at all costs," he said.

"With this in mind, and in light of current circumstances, we have resolved to stay on council for such time as there is an orderly transition to a refreshed council membership."

The school has appointed former federal court judge Ray Finkelstein, QC, to conduct an independent inquiry into the controversial sacking of Mr Brown.

A school spokeswoman said the council would be refreshed in coming months, once the inquiry was completed.

Tim Sharp, the former president of the Old Trinity Grammarians' Association, said there needed to be more independence and transparency around the appointment of council members.

"We are concerned that under the current constitution the existing council has the sole power to choose which council members succeed."

He said the school community's actions had been a last resort, after years of unsuccessfully trying to engage with council.