Public Health authorities expected the second round of testing - conducted over the weekend - to be the most likely time when another positive case would emerge, possibly from within the same household.

The close contacts must remain in quarantine until their 14 days were up, provided they continue to test negative.

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Of the 57 casual contacts, 56 have tested negative five days after their exposure risk and have been released from quarantine, with the final contact result still pending.

Director of Public Health Mark Veitch said it was still vital that anyone in Launceston with cold or flu symptoms get tested for COVID-19.

"Please don't be complacent about the risk of COVID-19 in Tasmania," he said.

"We need more people to get tested in the Launceston area this week, so we can be confident that COVID-19 is not in our community.

"If you live, work in, or visit Launceston, particularly Newnham and surrounding suburbs, please get a test if you have any cold or flu symptoms, even very mild."

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A mobile testing clinic in the Newnham TasTAFE car park on Alanvale Road will operate from 8.30am to 3.30pm every day this week, including for walk-in or drive-up testing.

The Launceston testing clinic at 246-248 Wellington Street is open daily from 8.30am to 3.30pm.

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