Two of the cases were flagged on Monday, and involved a man who attended a hospital emergency department and his household contact, with investigations continuing into how they contracted the disease, Xinhua news agency reported.
Brisbane's case, the first time the highly transmissible variant linked to Britain was recorded in a community in Australia, and several other cases of the new variants recorded in managed hotel quarantine, have put the country on high alert.
NSW Deputy Chief Health Officer Dr Jeremy McAnulty said everyone in the Northern Beaches needed to remain vigilant.
A man and a woman in their 40s who are residents of Sydney's Northern Beaches also tested positive and their source of infection remains under investigation.
"Close contact have been identified, isolated and tested", Dr McAnulty said. The injured woman arrived in Frankfurt by plane from Great Britain on December 20, where she and her relatives traveled to Baden-Württemberg.
This information will be updated on the website shortly.
NSW Premier Gladys Berejiklian warned community transmission is still ongoing in Sydney, meaning it was unlikely that restrictions would be eased this week.
"We know it tends to dip down as a result of the weekend in the early days of the week but we really need to have higher testing levels if we are to combat the rumblings that are still going on", Ms Berejiklian said.
"But it's so critical that we raise those testing levels, 14,700 is not really enough for where we're up to in the pandemic".