The premier's frustration with the lacklustre pace of the vaccine rollout was again on show on Tuesday as she announced NSW had recorded 19 new COVID-19 cases.

"The NSW government is trying to ensure that we have a sense of urgency across the nation about the vaccine rollout," Ms Berejiklian said.

The transmissibility of the Delta variant means some restrictions will have to stay, even after the current cluster is eradicated and Sydney ends its lockdown.

"When you know that you've got such a transmissible variant ... you do need to look at what life looks like because what we want to do is prevent ever having to go into lockdown again."

NSW must get 80 per cent of its adult population vaccinated before having a conversation about what "COVID-normal" looks like, the premier said.

That's five million people receiving 10 million jabs. More than two million doses have been administered in NSW so far.

The premier foreshadowed she would soon be announcing a plan to "step it up" and help the federal government distribute vaccines.

The number of new cases was just one higher than the previous day, despite health officials' fears of a surge in cases.

Ms Berejiklian added the caveat that "that could very well happen in the next few days".

The premier's comments came as deputy premier John Barilaro admitted the government "lost control of the Delta strain" last week.

"We've done a good job to this point, but there's no question, last week we lost control of the Delta strain," he told ABC radio.

"Hindsight is a beautiful thing. Absolutely you could have gone a week earlier, three days earlier, four days earlier, but the reality is ... that wasn't the advice."

Some 149 people have contracted the coronavirus locally since June 16, when the first case was reported at Bondi in Sydney's east.

Seventeen of the new cases were linked to previously confirmed cases, with seven already in isolation throughout their infectious period.

The source of the other two cases is still under investigation, though both work in Sydney's eastern suburbs, the epicentre of the outbreak.

Chief Health Officer Kerry Chant said a key indicator of success for the lockdown will be if all new cases were already in isolation.

She called on people who've visited the local government areas of Woollahra, Randwick, City of Sydney and Waverley to be vigilant for symptoms.

Some 67,000 people were tested for COVID-19 in the 24 hours to 8pm Monday, which Ms Berejiklian called "an outstanding result".

The government also announced financial support for small businesses hit by the lockdown.

Businesses will receive thousands of dollars in grants and the NSW Dine and Discover voucher program for state residents will be expanded.

Tuesday marks the third full day of a two-week hard lockdown for the Greater Sydney, Central Coast, Blue Mountains, Wollongong and Shellharbour regions.

Millions of people can only leave home for work that can't be done at home, to shop for essentials, for exercise, to seek medical care and for caregiving or compassionate reasons.

NSW Health issued more alerts for venues visited by COVID-19 cases, with the number of sites now at 250 and thousands of people now isolating.

They included the Doncaster Hotel at Kensington, Specsavers at Bondi Junction, McDonald's at Bondi Beach, Macquarie Bank in Barangaroo, Domino's Pizza Rose Bay, IGA Blaxland and the Meriton Suites Hotel at Mascot.

NSW Health has also alerted commuters who travelled on various Sydney trains and buses last week and Westfield Bondi Junction remains of particular concern.

More than 500 school students from South Coogee Public School are isolating after four of their classmates acquired the virus.

Another student, at Emanuel School in Randwick Sydney's east, attended school whilst infectious.

A positive case was also uncovered in the Rose Bay Secondary College community, sending around 1300 students and teachers into isolation.

Australian Associated Press