Coogee local Leah Stewart was attacked by a suspected great white shark while swimming in between the flags and close to shore at Coogee beach on Saturday.
The 35-year-old mother and teacher has undergone multiple surgeries, including the amputation of her arm, and remains in St Vincent's Hospital in a critical condition.
In a statement, her family thanked lifesavers, first responders, and hospital staff for caring for Ms Stewart.
"As a family we are shocked and devastated that this could happen to our beloved partner, daughter, and mother who is so full of life and energy," they said.
"Leah's injuries are severe and life-threatening. She will need extensive ongoing care, support and rehabilitation."
Her family have asked for support as Ms Stewart faces further surgeries in coming days, with her brother launching a fundraiser to aid in her recovery.
NSW Premier Chris Minns said the great white shark population would not be culled after the horrific attack.
"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.
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."
But experts say 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.
Mr Minns championed the idea of low-orbiting, AI-enabled drones becoming a permanent feature in surveilling shark activity.
Surf Lifesaving NSW public safety manager Brent Manieri confirmed drones would be allowed to fly across several beaches for the rest of the week.
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.
The NSW premier 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, noted there is 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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