However, the Berejiklian government says it won't define or dictate which types of workers should be classed as essential, leaving that crucial decision up to bosses and staff.

New testing rules were announced as it emerged a person who had travelled from Sydney's south to work on a construction site at Goulburn Hospital had tested positive.

NSW reported 89 new locally acquired cases and the death of a man in his 70s on Tuesday, as the number of infections linked to the Bondi cluster climbed past 760.

Twenty-one of the new cases had been infectious while in the community.

NSW Premier Gladys Berejiklian reiterated Sydney's lockdown - originally scheduled to end on Friday - wouldn't be lifted until that number was "zero or close to zero".

The outbreak continues to spread through the city's south-western suburbs, with 64 of the new cases linked to that region.

The NSW government will now force essential workers from the outbreak's epicentre in Fairfield to get tested every three days. Workers travelling out of other parts of Greater Sydney will require a weekly test.

Ms Berejiklian said she wanted to stop people from hotspots spreading the virus through their workplaces to other parts of the city - and regional NSW.

Authorities are again on high-alert to the potential spread of the virus from greater Sydney to regional NSW, after the Goulburn case was reported on Tuesday.

Health Minister Brad Hazzard said workers would need to carry proof of their test results, in case they were stopped by police.

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The Goulburn case has sparked fresh debate about which types of workers who should be classed as essential, as therefore free to travel, amid an unfolding health emergency.

The person who tested positive was a painter working on the construction of the new Goulburn Hospital, according to Goulburn Mayor Bob Kirk.

"The COVID disease doesn't ask people if they have a travel exemption or not, it just attaches to whoever it can," Mr Kirk said on Tuesday.

"But I understand he is a painter ... I don't know how that qualifies as essential right now."

"I know there are more than a few painters around this place that could step up if needed."

Pressed on issue of essential work on Tuesday morning, Mr Hazzard said "to try and define that is very challenging".

Mr Hazzard said it would be left up to the employer and employee to determine if their job was essential.

However, he urged people in the virus hotspots to avoid travelling if they could.

"If you don't need to have someone come from an area that is suspected and obviously has major COVID concerns presently, then perhaps it might be an idea to have arrangements for a worker from another area," he said.

NSW Chief Health Officer, Dr Kerry Chant said essential workers, from her perspective, were those who made up the health network.

"We have to balance having no work force," Dr Chant said. "This is about balancing competing risk and benefits."

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