While some children may be eligible for a face covering exemption, Holsted said other students may not want to follow the rules.
Holsted said schools must treat this situation as they would towards uniform and sunblock rules.
"For any child or young person who is failing to comply with the legal requirement, and who is not exempted, you will be able to apply or agree your own school policies to manage this behaviour, in the same way you might enforce sun hat and sunblock rules, uniform rules, etc."
The Government has made changes with how schools deal with Covid, including increasing isolation time for confirmed cases, scrapping the casual plus contact, and treating vaccinated and non-vaccinated confirmed cases the same.
High School principals spoken to by the Herald say they are struggling to find the new rules, or find the changes complicated and mixed with outdated information.
Macleans College principal Steven Hargreaves heard about changes via a daily bulletin and zoom call but has struggled to find the updated information anywhere online.
He said principals had been "hung out to dry" with little clarity.
"We need to know exactly what now constitutes a close contact and have those letters ready to go to those affected straight away."
Holsted on Thursday also outlined what staff members should do if a Covid-19 case arises in their school.
Schools must contact their regional Director of Education or their region's Covid-19 contacts as well as those who may be close contacts to the student or staff member.
From there, schools must identify a number of things including if the student was wearing a mask, if they were at least 1.5 metres away from other students and who they spent their break times with.
"We are working with the Ministry of Health to update our processes and detailed guidance for contact tracing," Holsted said.
Meanwhile, an update on masks was also given. Anyone who is covered by the vaccine mandate, including paid and unpaid staff, are now required to wear a medical-grade face covering.
"The mask is only required to be worn while in a public-facing role.
"However, while masks are not required to be worn by staff in staff rooms, we would strongly encourage they are worn in any indoor setting where people are in close contact," she said.
