The announcement came after one new case was recorded in Batemans Bay and another in Cooma on Monday morning, and the first case on the South Coast for more than a year.

In a statement, SNSWLHD said the contact tracing team had notified close contacts of the Batemans Bay case.

"Our contact tracing team is working closely with the [Batemans Bay] case who is quite ill as a result of their COVID-19 infection," the statement said.

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Deputy Premier John Barilaro told Australian Community Media the positive COVID-19 case at Batemans Bay was "complex" and investigations were continuing.

"I have been told some of the scenario and what it looks like," he said.

"There could be concerns and we need to get that out there sooner rather than later."

He said he would enquire within NSW Health to provide information as soon as possible.

"I understand the anxiety is worse around not knowing, than knowing," he said.

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More than 24 hours since the cases were announced the community was still waiting for an update on exposure venues.

SNSWLHD explained NSW Health only listed venues of concern if there was a chance a member of the public had come in to contact with a person who was infectious with COVID-19.

"We understand how important clear and timely communication is at a time like this," the statement said.

"Rest assured, we will always share case and venue of concern information as soon as we can. Contact tracing and case interviews can be complex and can sometimes take days to complete.

"Our teams are working long hours to thoroughly investigate every case to keep the community safe."

The community was reminded the best way to help the contact tracing team was to use the Service NSW QR code to check in to every venue visited.

A drive through testing clinic was established at Hanging Rock oval on Beach Road, open from 8am to 5pm.

To find your nearest testing clinic, visit the NSW Health website.

To book a vaccine visit the eligibility website.

More to come.