The vast majority of people in NSW are living under stay-at-home orders and a one-week snap lockdown has been applied to Bogan, Bourke, Brewarrina, Coonamble, Gilgandra, Narromine, Walgett and Warren LGAs, as authorities scramble to identify all exposure sites.
Ms Berejiklian says Police Commissioner Mick Fuller is working with health officials on a range of measures to let the government know "what he needs to clamp down on compliance".
"Compliance is a major issue ... even when 99 percent of people are doing the right thing, that one percent (doing the wrong thing) can cause a setback for everyone else," she told Sydney radio 2GB on Thursday.
"So we're beefing up our police powers to be able to clamp down on those things,."
An NSW crisis cabinet meeting on Wednesday night reportedly adopted tough new measures to close loopholes that saw people travelling out of Sydney, allowing the virus to bleed into the regions.
On Wednesday a 52-year-old Sydney man was charged at Lismore Hospital with breaching public health orders after travelling to Byron Bay on the north coast while Covid positive, plunging the region into lockdown on Monday.
Ms Berejiklian said "nobody would think it's common sense to travel hundreds of kilometres from home ... during a lockdown in order to look at a property".
Cabinet also reportedly decided an additional 500 defence force troops will be brought in to enforce compliance and help with contact tracing and more police will patrol Covid hotspots.
The lockdown on Wednesday night was triggered when a man was diagnosed with Covid after being released from Bathurst jail on Monday and travelling 500km west to Walgett, visiting Dubbo and Bathurst en route.
Bathurst jail is the first in NSW to record a Covid-19 positive case this year.
The newly locked-down regional areas join Dubbo, Tamworth, the Northern Rivers, Armidale, Newcastle, Lake Macquarie, Maitland, Port Stephens, Singleton, Dungog, and Muswellbrook.
The Hunter region lockdown that's due to expire at midnight is expected to be extended with 53 cases in the area and a growing list of exposure sites.
The virus is also infiltrating Sydney's inner west and there's speculation the Bayside and Burwood local government areas - where cases are on the rise - could be the next to have tighter restrictions imposed.
NSW reported 344 new locally acquired cases in the 24 hours to 8pm on Tuesday.
Meanwhile Wheeler Heights Public School on Sydney's northern beaches is closed on Thursday for cleaning and contact tracing after a student tested positive to Covid-19.
All staff and students are asked to self-isolate and follow the NSW health advice and protocols.
Luddenham Public School in Sydney's west is also closed after two students tested positive to Covid-19.
