AT least 50 people were infectious in the community among 199 cases detected in the 24 hours to 8pm on Monday evening.
More than 104,000 tests were carried out across the state yesterday, and comes the day after a record 117,000 swabs on Sunday.
There are currently 250 cases admitted to hospital, with 53 people in intensive care, 20 of whom require ventilation.
Ms Berejiklian said it was crucial that vaccine doses were focused in the eight local government areas subject to the strictest lockdown conditions and home to the most rampant spread.
NSW Health said 88 of the local cases are linked to a known case or cluster, 67 are household contacts and 21 are close contacts.
Transmission continues to centre around households and workplaces in Sydney.
"We don't know if it's peaked or if it's going to get worse," Ms Berejiklian said.
Ms Berejiklian said the government had been exploring incentives "for some time", and had wanted to make clear to Sydneysiders what life beyond lockdown could look like if vaccination and case numbers co-operated by the August 28 deadline.
"On the current rate that we're doing we should be able to get there with the jabs," she said.
"We're really focusing on what people really want at this stage," she said.
"They want certainty they can move around freely, send their kids to school, go to work.
"We believe based on experience overseas that allowing people extra movement or extra activity if they've been vaccinated is the greatest incentive of all."