NSW health officials are working desperately to track the origins of a rapidly growing COVID cluster at a school in Sydney’s north-west.

There were eight new virus infections linked to Tangara School for Girls in Cherrybrook on Tuesday, after nine on Monday.

The school now has 17 confirmed cases after the first infection was discovered in a student on Thursday. But the “patient zero” who brought the virus to the school has so far proved a mystery.

Premier Gladys Berejiklian reiterated a warning to non-government schools on Tuesday to coronavirus restrictions.

“Schools, in particular non-government schools, cannot undertake those extra-curricular activities that you do outside of a pandemic – and I can’t make that message stronger,” she said.

She said institutions needed to ensure there were no off-site gatherings where mingling could occur.

“Every organisation, every entity needs to abide by the COVID-Safe plans, because otherwise we risk having a surge in numbers [and] new clusters, and no one wants to see that.”

Gladys Berejiklian says NSW faces a “daily battle” to keep the virus under control. Photo: AAP

The school’s senior campus will be closed until August 22, but the junior campus will reopen on Wednesday. All secondary students and staff are in self-isolation and being tested.

The cases linked to the school were among 22 new virus infections confirmed in NSW on Tuesday. That’s the highest in four months – since 29 were confirmed on April 16.

“It is a daily battle in NSW; we have to be on our toes, we are in a state of high alert,” Ms Berejiklian said.

“My anxiety has not subsided in relation to what a knife’s edge NSW is on.”

Four of Tuesday’s cases are returned international travellers in quarantine, while two more are in people who came to NSW from Victoria.

Among other cases of concern in NSW were three at schools on the south coast.

NSW health authorities say one student from Batemans Bay Public School and two students from Batemans Bay High School have tested positive to the virus.

“All staff and students are asked to self-isolate while contact tracing occurs,” a statement from the high school read.

“They’re likely to both reopen on Wednesday for on-site teaching and learning,” the NSW Department of Education’s Murat Dizdar told the ABC.

NSW health said two of the infected people were contacts of a previously reported case from the Batemans Bay Soldiers’ Club. This brings the number of cases associated with the club to 10 – although they were the first reported linked to that outbreak in three weeks.

NSW Health will set up a pop-up coronavirus testing clinic in Batemans Bay for the rest of the week.

NSW chief health officer Kerry Chant has urged people to avoid large gatherings and this week admitted older school students are more likely to transmit the virus.

“We still know and believe younger students such as primary school students are not likely to be infecting [others] but as you get older … an 18-year-old at school is more like an adult in terms of their characteristics, the risks of transmission,” she said.

Premier Gladys Berejiklian said the state remained on high alert.

“We are in a pandemic – every organisation, every entity needs to abide by the COVID-safe plans,” she said.

“I don’t want people living with the guilt of passing on the disease or causing the spread because they could’ve prevented something from happening.”

Eight COVID-19 patients in NSW are in intensive care, with six on ventilators.

-with AAP