NSW may permit private venues to bar those not vaccinated for COVID-19, while the state has recorded zero new local cases of the virus.

NSW has recorded no new locally acquired cases of COVID-19, as Premier Gladys Berejiklian suggests the government may permit venues to ban entry to those who decline to take the COVID-19 vaccine.

Parents, staff and students at NSW schools, meanwhile, will not be obliged to wear masks when term one begins later this month.

NSW recorded zero new locally acquired cases of COVID-19 in the 24 hours to 8pm on Sunday, as well as eight cases in hotel quarantine.

However, the tally came from fewer than 9000 tests, prompting NSW Health's Dr Jeremy McAnulty to plead for an uptick in testing numbers.

Ms Berejiklian has previously flagged the possibility of easing restrictions on Greater Sydney this week but only if testing rates are sufficiently high.

"The drop in daily testing numbers is of concern and NSW Health renews its calls for people to get tested if they are experiencing even the mildest of symptoms," Dr McAnulty said in a statement on Monday.

"The best thing we can do for our friends and family is to get tested."

NSW recorded six new local cases of COVID-19 in the prior 24-hour period, five of which were household contacts of a previously confirmed case. NSW Health has now genomically linked those cases to the 35-person Berala cluster.

The sixth case was a Concord Repatriation General Hospital staff member who worked in the cardiology and radiology wards and may have been infectious on January 12, 13, and 14 but had minimal patient contact.

Ms Berejiklian also on Monday broached the possibility of barring those who decline the COVID-19 vaccine from government-run buildings, as well as permitting private venues to adopt similar measures.

As the planned February rollout of the vaccine nears, the NSW government is considering a data-sharing partnership with the federal government that would help residents prove they have been immunised.

Ms Berejiklian has previously suggested the Service NSW smartphone app could show a tick when a person is vaccinated, enabling venue entry.

"The more people that are vaccinated, the greater likelihood we can have a return to normality as we know it," Ms Berejiklian told 2GB radio.

"Already airlines have indicated that if you're not vaccinated you can't travel overseas and I think that'll be an incentive to a lot of people.

"But we'll also consider whether we allow venues ... make up their own rules if they have a business or run a workplace about what they feel is COVID-safe."

The NSW government on Monday also announced school students and staff would not be obliged to wear masks at school in term one - but those aged 12 or over would need to wear masks on public transport.

Parents remain discouraged from entering school premises without a clear reason. However parents of children in kindergarten and years one, two and seven are permitted to attend their child's first day of term.

Victoria, meanwhile, will from 6pm on Monday fully open its border to 16 local government areas in southern NSW, and also ease restrictions for visitors from all but 10 local government areas in Greater Sydney.

Those visitors will be required to seek COVID-19 testing upon arrival in Victoria and self-isolate until they receive a negative result, but will not be barred entry.

Residents of local government areas including Parramatta, Liverpool, Fairfield, Burwood and Strathfield remain locked out of Victoria.

Victoria has gone 12 straight days without a new local coronavirus infection and residents stuck in Brisbane are now free to travel back to the state.

One COVID-19 patient in NSW is in intensive care.