The state recorded zero locally-acquired COVID-19 cases in the 24 hours to 8pm on Sunday and three cases in travellers in hotel quarantine.

The tally came from 8689 tests, prompting NSW Health to say that virus testing rates urgently needed to lift.

"Low testing numbers remain a concern. We are strongly urging people across the state to come forward for testing with even the mildest of symptoms," NSW Health's Jeremy McAnulty said on Monday.

After a COVID-19 case leaked from New Zealand's hotel quarantine system and was uncovered in a 56-year-old woman in the Northland region, NSW Health issued an alert for recent Kiwi arrivals.

Those who arrived in NSW from New Zealand since January 14 should check the venues of concern listed by New Zealand health authorities and, if necessary, follow the country's health advice.

They have also been told to seek testing in NSW with even mild symptoms.

New Zealand travellers are permitted to enter NSW without undergoing 14 days of hotel quarantine due to "travel bubble" arrangements.

The New Zealand alert comes as interstate travel restrictions on NSW residents began to ease over the weekend.

Victoria's border has reopened to almost all of Sydney, barring the Cumberland local government area, which takes in Berala.

All Greater Sydney LGAs - as well as Wollongong and the Blue Mountains - were downgraded to "orange" on Victoria's health alert system from Friday.

People travelling to Victoria from an "orange" zone will need to apply for a permit, get tested within 72 hours of their arrival and isolate until they receive a negative result - but they will not be barred from entry.

Western Australia also relaxed border restrictions, with NSW residents no longer banned from entering the state. However travellers will still be required to self-isolate for 14 days and get a COVID-19 test.

Tasmania has also relaxed restrictions on large parts of Greater Sydney.

Australian Associated Press