Tracey West, her husband and her daughter had lived at the property for five years when they were told in February - before the eviction moratorium was put in place - that their lease would not be renewed and they had 42 days to vacate.

The family did not oppose the eviction, but have been unable to find a new rental despite applying for about 30 properties.

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They received an extension from the Magistrates' Court until April 21, when a court application will be made for the bailiff to change the locks on the property.

Ms West said that without many open inspections occurring for rentals due to social distancing, and with few allowing them to keep their two dogs and two cats, they had been unable to find anywhere else to live.

"A lot of inspections are cancelled on the day it's meant to go ahead, it's just been an absolute nightmare," she said.

"There was never any contention over the eviction, but when we came back and said we couldn't find another place, and asked for an extension of time, they tried to refuse it."

The landlord intended to move into the property and renovate it, having recently relocated to Tasmania from the mainland.

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The moratorium announced by Premier Peter Gutwein started on April 3, after the eviction notice was given.

Ms West has contacted Housing Connect, but there appears to be a significant caseload at the moment due to coronavirus-related demand. Her matter was deemed "urgent".

She said they just wanted some compassion as they believed they had been good tenants, had not fallen behind in rent and had no means of transporting their belongings at this time.

"No one can tell us what's going to happen on Tuesday," Ms West said.

The Tenants' Union of Tasmania analysed the case and found that the eviction was legally acceptable, but they hoped the landlord "could have compassion" to delay moving in until after the pandemic.

There was some hope that the court could deem the application with the bailiff as "non-urgent", but it appears the matter will be confirmed on Tuesday.

Senior solicitor Ben Bartl said it was an "unfortunate" situation.

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"Our view would be that if the landlord doesn't have to move in immediately, he should have some compassion towards the tenant given that she has nowhere else to go and we're living through a health pandemic," he said.

"This case has fallen through the cracks because some people who are in a similar position have either found somewhere else to move to, or the landlord has waived their right to kick the tenant out."

The Tenants' Union has advocated for similar laws to Victoria where tenants have the right to keep a pet, unless their landlord makes a successful refusal application with the civil tribunal.

Harcourts Launceston, which manages the property, stated it had followed all directions from the court.

General manager of sales and property management Jayne Harwood said that under the pre-coronavirus conditions, it was a standard legal course of events.

"There's a process under the legislation - and it does take quite a bit of time. This has started before current circumstances, we have been in contact with the Magistrates' Court and they advised us to follow the procedure which we have done," she said.

"All real estate agencies are aware that we must make sure we're following the legislation of the day, and we have complied with that.

"If after 42 days' notice the tenant has not vacated, that's when we go to court to secure vacant possession."

Ms Harwood said Harcourts Launceston has 26 vacant rental properties at the moment at an average of 25 days' on the market, which is slightly higher than usual as fewer people are choosing to move house at the moment.

She said there were "a number of pet-friendly owners", but discretion was entirely a matter for individual landlords.