There are four new cases in NSW, including three healthcare workers at two Sydney hospitals and a returned overseas traveller in hotel quarantine.

The three were diagnosed during investigations into an emergency department doctor reported on Saturday who worked at Sydney's Concord Repatriation General Hospital and Liverpool Hospital while infectious.

Authorities are scrambling to determine whether they contracted the virus from a contaminated object.

Premier Gladys Berejiklian says it's a scary reminder of how contagious the virus is.

"We always need to be on our guard because this disease is like none other than we've experienced," she told reporters on Monday.

"Even if you're wearing a mask, you can still get it, and you can still unintentionally give it to others so it's important for us to stick to all the rules, all the health advice we've been given, not just one part of it."

Another case, a visitor to a hospital emergency department where the doctor worked or sought treatment, will be included in Tuesday's numbers, taking the cluster to five.

Patients considered close contacts and all staff at Concord and Liverpool EDs at the same times as the positive cases are being isolated and tested.

Authorities are concerned by the likelihood at least one of the new cases caught the virus while both parties were wearing masks.

"For some of the cases there isn't that clear-cut direct contact without a surgical mask," NSW chief health officer Kerry Chant told reporters on Monday.

"We are exploring avenues of whether there could be fomite transmission.

"What that means in lay terms is if your hands are contaminated, and then you're touching computer screens or touching pens and pencils pieces of paper, can you actually transmit the virus."

The three newly-reported health workers reported having no symptoms while at work and also wore personal protective equipment while caring for patients.

Dr Chant said the state's hospitals were still operating safely and effectively, and it was important NSW residents don't delay urgent care.

Meanwhile, two Sydney schools are closed after students tested positive while the number of cases linked to a CBD gym has grown to 64.

Kincoppal-Rose Bay School in Sydney's east was closed for on-site learning on Monday after two year 7 students were among the 10 new cases reported in NSW on Sunday.

Lidcombe Public School in western Sydney was closed on Monday but will reopen on Tuesday after NSW Health confirmed a student who initially tested positive does not have COVID-19.

All close contacts have since been notified and released from isolation.

In a statement, the school said NSW Health was apologetic for any "inconvenience or distress" the disruption may have caused.

Despite a number of outbreaks in schools in recent months, Ms Berejiklian on Monday confirmed school formals and graduations would be allowed to go ahead in Term 4.

Health authorities are working with the education sector to come up with appropriate COVID-safe plans, but Dr Chant has hinted she may allow dancing, despite the activity being banned at weddings.

Australian Associated Press