There has been an increase in the number of people arriving Tasmania from Victoria since the state's recent spike in COVID-19 cases.
A further 270 new cases of COVID-19 were diagnosed in Victoria on Tuesday bringing the state's total number of active cases to 4224.
Tasmania Police Commissioner and State Controller Darren Hine confirmed on Tuesday there had been a recent rise in arrivals from Victoria.
"We know there are thousands of former Tasmanians living in Victoria who have some connection with Tasmania and want to come back," Commissioner Hine said.
"Our message is, if you can stay in Victoria and abide by their restrictions, please stay there."
Commissioner Hine said there were currently almost 1000 people being monitored in home quarantine and almost 600 people quarantined in government-run hotels.
He said police were coming up on 20,000 compliance checks on those in home quarantine since the pandemic began.
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Since Victorians were banned from entering Tasmania without an exemption last Thursday, four Victorians who have attempted to enter the state have been turned around and as of Tuesday morning a further four who arrived on the Spirit of Tasmania were being evaluated.
"Essential traveller applications have also been highly scrutinised for those people from Victoria, and to date since last Thursday there's only been one application that has been approved ... where they have had to attend to a hospital situation," Commissioner Hine said.
"It's a very high bar they have to meet.
"If they can get those services from anywhere else in Australia, that is our preference."
Commissioner Hine said Tasmanians who needed to travel to Victoria for medical reasons could be quarantined at home upon their return if hotel quarantine would be adverse to their health.
"They need medical evidence to support their application to be able to quarantine at home," Commissioner Hine said.
"We are taking a very humanitarian approach to make sure we are not jeopardising their health, for them to travel from Tasmania to get the help that they need."
But this does not appear to have been put into practice, with an Ulverstone woman who travelled to Melbourne for heart surgery forced into hotel quarantine upon returning to Tasmania last Friday.
The woman and her husband, who did not wish to be identified, said on Monday they had been given food they cannot eat due to their medical conditions and have only been allowed one 10 minute exercise period since arriving.
When asked what she expected as a minimum standard for access to fresh air and space to exercise for state-run quarantine facilities, Health Minister Sarah Courtney said the most important thing to remember in regards to hotel quarantine was it was being done to try and keep Tasmanians safe.
"We know quarantine hotels do have a high level of risk - we've seen that in other jurisdictions," Ms Courtney said.
"We need to ensure we are balancing the health and welfare of Tasmania with the welfare of the Tasmanians and the visitors that are in those hotels.
"We are working closely with service providers and Communities Tasmania to ensure people that are in those facilities are given the support they need."
Ms Courtney said the government would monitor if it was sustainable for the state to continue funding hotel quarantine.
"We know coronavirus is going to be with us for a long time and so we need to be able to have systems in place that are sustainable. We will take advice on it should we need to change policies in the future," she said.
Meanwhile, Tasmanian public health authorities are closely watching New South Wales as a new cluster of cases centered on the Crossroads Hotel in Casula is being investigated.
Public Health director Mark Veitch said he and his colleagues in other states would be watching NSW with interest and some concern.
When asked of hotel quarantine should also be applied to people arriving in Tasmania from NSW, Dr Veitch said the level of risk was constantly being assessed.
"What we need to get to is a situation where we can process the hotspot," Dr Veitch.
"What's a hotspot in Western Sydney today may be a hotspot in Southern Queensland tomorrow."
Ms Courtney said the government would not hesitate to put additional restrictions on other jurisdictions if this was the advice of public health.