Nearly 400 cars have been turned around along the NSW border by police, since the closure with the Victorian border came into place.
Riverina Police District Acting Commander Adrian Telfer said people would be turned around at the border unless they had the new permit linked to the updated public health order.
"We've turned around in the vicinity of 380 motor vehicles since the commencement of this operation, and by and large the community has responded very positively to all of the checkpoints," he said.
"Please expect delays - we certainly recommend you avoid travelling during the peak times.
"We have seen this morning a number of people approach our checkpoints across NSW with permits that are now expired.
"We expect as they [police] become more familiar with the process ... that will improve time spent in the line."
Detective Inspector Telfer said police had worked with people in many instances to help them apply for the new permit at the checkpoint, with there being 300,000 vehicle movements since the closure started.
"We do have a number of people in the Riverina who are currently in isolation, having travelled from Victoria ... we will be doing random checks," he said.
Police officers were this morning following up one instance where a resident in the Riverina was meant to be at home self-isolating after travelling, and was not found at their address.
Murrumbidgee Local Health District has around 150 staff who usually work in NSW, but live in Victoria, who have been affected by the tightening of the border closure.
Chief executive Jill Ludford said her staff who lived in the border area were not removed from the impact of the new public health order.
"They can only access that permit if they're working on the front line and can't work from home," she said.
"[The permit] is to access time-critical health care, health care that is not available in Victoria; for education reasons, where they can't study at home; and for work-related activities, again where people can't work for home.
"Those are the only times people will be given a permit.
"For people who need to still have time-critical medical care, they can always go across the border ... but they will need to self-isolate and their families will need to self-isolate upon returning to NSW.
"The restrictions are in place to keep the residents of NSW safe.
"I think one of the issues that we saw with the former order was once people in those border towns were either side of the border, they could actually keep travelling - that put us at heightened risk.
"Now we've seen very clear communication in those permits ... if you're going from NSW across to Victoria, you can only travel in that border zone.
"Tightening that up ... I think is really important.
"I understand for people living in that area, close to the Murray River, the difficulties that places on their everyday life."
Ms Ludford said the number of positive COVID-19 tests remained at 49.
"We had additional cases over the last couple weeks - three cases in Albury and one returned traveller from the Snowy Valleys shire," she said.
"We've now clocked up nearly 30,000 tests, people coming forward from our community to be tested .. since we started testing.
"We've really seen the numbers ramp up enormously in the last week; we've done 500 additional tests just in the last week."
Ms Ludford said people were concerned with recent outbreaks in Victoria, and 13 cases in NSW as of Tuesday.
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"We've been able to ring-fence those new, seeded outbreaks," she said.
"I understand you are all concerned that the COVID outbreaks have come across into our region, but I just want to reassure you that we have increased our staff to undertake more testing.
"Only a month ago we were testing about 2000 people a day ... we've now doubled that to 4000 people a day.
"I keep hearing people say 'We don't have COVID in our region'. You don't know that, and we always have to be alert and aware that it could come, at any time."
Anyone who wants to be tested should contact the Murrumbidgee COVID-19 Hotline on 1800 831 099.