The federally protected species is suspected to have been responsible for an attack on Leah Stewart, a 35-year-old mother, who sustained critical injuries at Coogee beach on Saturday.
NSW Premier Chris Minns has overruled Agriculture Minister Tara Moriarty after she left the door open on culling as a shark mitigation strategy.
"When it comes to shark culling, the truth is the great white shark is protected," he told reporters on Monday.
"We're not going to be contemplating a cull.
"I'm not convinced it would work ... and certainly we haven't received evidence or information it would work."
He noted there needed to be a rethink of how the issue of sharks is approached after several bull shark attacks in January.
On Saturday, the woman was swimming between the flags at about 11am when she was bitten by a suspected great white shark, sustaining flesh wounds to her leg and arm.
She remains in hospital in a critical but stable condition.Â
The attack reignited calls to cull shark populations to protect swimmers, with former prime minister Tony Abbott joining other politicians coming out strongly in favour of the measure.
"It's so wrong that we don't cull sharks after attacks," he said in a video he posted on his social media.
"It's so wrong we don't put people before sharks."
Ms Moriarty had not expressly ruled it out on Sunday, saying "nothing is off the table in terms of how we keep the community safe".
But experts warn there is little evidence shark culls keep ocean-goers safer.
Adelaide University environmental science program director Brianna Le Brusque said harmful encounters with the predators were tragic and cull discussions an understandable response.
There was no science on how many animals would need to be removed to keep swimmers safe nor evidence it would meaningfully improve community safety, she said.
Surveillance methods, including employing spotters from vantage points to alert swimmers, were more effective, Dr Le Brusque told AAP.
On Monday, Mr Minns championed the idea of low-orbiting, AI-enabled drones becoming a permanent feature in surveilling shark activity.
The Civil Aviation Safety Authority has given a temporary exemption for aerial surveillance of Coogee Beach in the wake of the attack.
Surf Lifesaving NSW public safety manager Brent Manieri confirmed drones would be allowed to fly across several beaches for the rest of the week.
"We will be operating ... to ensure there's a level of aerial surveillance that the community can feel safe and assured in when they want to come back down and have a swim," he told ABC on Monday.
The beach is about eight kilometres from Sydney Airport.
Mr Manieri said negotiations were ongoing with the NSW government to fly drones across all of the state's coastline to protect the public.
Shark nets, another method of separating humans from marine predators, are set to be installed at the start of September.
Mr Minns reiterated his support for shark nets as a useful deterrent and signalled they could remain all year round instead of summer months only.
RMIT University fellow Rebecca Olive, a senior researcher in sport and leisure, said there was more than one type of shark net, with some fully-enclosed and others free-floating.
"Whales, dolphins, turtles, rays and birds all get caught in them," she said, adding that the effectiveness of the nets in halting shark attacks was questionable.
Coogee Surf Life Saving Club is hosting a community gathering for anyone affected by the shark attack on Monday evening.
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