The woman, aged in her 30s, is the fifth person in the state confirmed with the new virus strain.
The fully vaccinated woman arrived on flight QR908 from Doha on Thursday last week and travelled by private car to the Central Coast.
Everyone on that flight is considered a close contact who need to get tested immediately and isolate for two weeks.
Two more people on that flight have already been confirmed to have the virus and neither of them had been in southern Africa.
Urgent genomic testing is underway to see if they have the Omicron variant.
A third case from that flight who has tested positive is believed to have a different, earlier variant of the virus, but is awaiting genomic confirmation in Broken Hill.
While the four people who had tested positive for Omicron after arriving from overseas on the weekend have been quarantined, the woman was able to leave the airport after arriving on Thursday last week before the rules were changed.
She visited several supermarkets, shopping centres and restaurants in Sydney and the Central Coast on Friday and Saturday before NSW Health directed recent arrivals from a number of countries in southern Africa into isolation.
She's now isolating at home on the Central Coast.
People who were at a number of locations at the same time as the woman on Friday and Saturday are casual contacts who should immediately get tested and isolate until they receive a negative result.
People who return a negative result are encouraged to get tested again if symptoms develop.
NSW Health has listed numerous shops the woman visited in Westfield Parramatta, as well as a supermarket at Top Ryde.
She also visited a grocer and two fast food restaurants in Wyong and North Wyong on Friday night, as well as a Wadalba supermarket.
On Saturday afternoon she visited another supermarket at Toukley.
People using QR codes to check into venues via the ServiceNSW app can find case alerts in their check-in history.
Health Minister Brad Hazzard said the woman "came in before the new arrangements ... so she has been out in the community and (NSW) Health is now investigating that".
"She has essentially been out in the Central Coast area," he told Seven News.
NSW recorded 179 new cases of COVID-19 and there were three COVID deaths recorded in the 24 hours until 8pm on Monday, ending a four-day run of zero deaths.
The latest COVID deaths include a western Sydney man in his 40s with underlying health conditions who died at Nepean Hospital.
A man in his 50s died at Tamworth Base Hospital and a woman in her 60s died at St Vincent's Hospital.
NSW Health said 62,166 tests were conducted in the past day.
Some 94.6 per cent of people aged 16 and older have had one dose of a COVID-19 vaccine, while 92.5 per cent are fully jabbed.
More than 81 per cent of teens aged 12-15 have had one dose of a vaccine, while 76.7 per cent of them have had two doses.
There are 160 people in hospital with COVID-19, 26 are in ICU and 11 are ventilated.
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