26 new cases of COVID-19 recorded across state, taking total active cases in Tasmania to 52

Public Health chief medical officer Mark Veitch said most of these cases are likely to be the Omicron strain.

He said all current cases in Tasmania could be traced, but warned that in the coming days the state was likely to see cases from unknown sources arise.

Of the 26 new cases, a majority are from New South Wales, some are from Queensland, South Australia and Victoria, and a few of the new cases are close contacts of those who are already in quarantine.

One of the active cases in the North West has been hospitalised but it was stressed that this infected person was not sent to hospital because of coronavirus.

The case went to hospital because of a fall and tested positive for coronavirus whilst there.

Dr Veitch said cases would continue to increase in Tasmania.

He did not rule out border closures.

"Up until 8 o'clock last night we had not identified a case that had appeared to come from an unknown source in Tasmania but... in the coming days we will start to see occasional cases of people who have been infected in Tasmania," Dr Veitch said.

"Be mindful of community risk ... reduce the risk of you, if you have an infection, of infecting others."

Meanwhile Premier Peter Gutwein said travellers were still required to be tested for coronavirus 72 hours before travel but the government was considering advice around rapid antigen testing.

"There is no change in terms of the 72 hour pre test...people who are arriving from interstate, I know it can be difficult but you need to get that test if you are coming to Tasmania from a high risk location. Ensure you get that test."

In terms of booster shots, Mr Gutwein said Tasmania is leading the nation, with more than 45,000 Tasmanians having already received their boosters, which represented 10 per cent of those who are eligible.

Mr Gutwein said planning is underway if the timeframe for booster shots was reduced from five months to three or four.

"We have assurances that we will have the necessary doses should that occur, and our state run clinics will expand to meet increased demand," he said.

Mr Gutwein also encouraged Tasmanians to purchase at home rapid antigen test kits which provide a further safeguard against COVID-19.

He said these home tests could be used to provide a positive indication to isolate immediately, prior to seeking the most accurate PCR test.

"I can confirm that Tasmania has already ordered a further 100,000 rapid antigen tests which can be utilised in home or business settings. We expect those to arrive in coming days, we already have a stockpile in hospitals should we need to use them in high risk settings," he said.

"I do want to make the note that these rapid tests are available in supermarkets and pharmacies. We have had a ring around this morning to check supply and my understanding is that they are widely available.

"It is another safeguard that people can use to do a quick test for Covid. If you get a positive result, make sure you isolate and organise a PCR test immediately.

"If you are not well simply isolate, book into a clinic, get a test. The rap test can provide an indication, but if it is positive, get a PCR test and isolate until you do so."