NSW has recorded yet another record daily number of COVID-19 cases, but Premier Gladys Berejiklian insists she won't introduce harsher lockdown measures unless they have a proven impact on transmission of the virus.

NSW reported 356 new local cases of COVID-19 and at least 97 of those people were circulating in the community while infectious.

Four people have also died - a man in his 70s, a man in his 80s and a woman in her 80s, as well as a returned traveller in his 80s unlinked to the current outbreak. All were unvaccinated.

Infection numbers in NSW have remained stubbornly high despite an increasingly tight lockdown, particularly in Sydney's west and southwest.

Sydney and surrounds are in lockdown until at least August 28, while the Hunter, Byron Bay, Armidale and Tamworth are in snap lockdowns.

Ms Berejiklian said her government would be glad to consider further measures to limit movement and interaction, but few remained that were proven to reduce virus transmission.

Curfews were listed among this category.

She said that, given the virulence of the Delta variant and its prevalence among essential workers obliged to leave home, a focus on the rapid vaccination of locked-down communities was preferable.

However, compliance with health orders remains problematic.

It comes after a virus-positive Sydney man travelled to Byron Bay against the rules and purportedly refused to use QR code check-ins. The incident has sent the northern rivers region into its lockdown.

"Policy positions that may have worked in the past aren't going to have effect with Delta, it's something we need to accept," the premier said on Tuesday.

"Short of not having authorised workers do what's necessary, it's really difficult to get to lower cases without that targeted vaccine strategy.

"Delta is different, we need to treat it differently, and NSW doesn't have any intention of putting in strategies that aren't going to work.

"If we thought they'd have a significant or even marginal impact, of course we'd do those things, but there is no evidence to suggest that."

More than 80 per cent of the NSW population is now in lockdown as the state struggles to curb the spread of the Delta strain.

The death toll from the current outbreak now sits at 32. There are 60 COVID-19 patients in intensive care, with 28 ventilated.

Ms Berejiklian again said her government's aspiration remained "COVID zero", as per national cabinet, but also that NSW would consider partially easing restrictions once it reaches six million vaccinations.

About 4.5 million jabs have been administered so far.

Prime Minister Scott Morrison on Tuesday said he wanted all Australians around the dinner table with their families on Christmas Day.

"We have one of the lowest death rates in the world from COVID and we want to be able to continue to achieve that as best as we possibly can as we continue through this suppression phase," Mr Morrison said.

"That's why there aren't any shortcuts to lockdowns."

Chief Health Officer Kerry Chant also revealed four of the eight residents at St George Aged Care Centre have caught COVID-19 from a staff member. All eight residents were fully vaccinated.

While locked-down Armidale and Tamworth have not recorded new virus cases, Dr Chant said new infections were uncovered in the Hunter. A case unlinked to the travelling Sydney man was also found in Byron Bay.

"Once you've got that force of infection, it's really hard to turn it around ... that's why I think we all need to redouble our efforts," Dr Chant said.

© AAP 2021