The relocation of the drive-through coronavirus testing clinic from the Elphin Sports Centre to near the Esk Market grounds in Inveresk is part of the process in allowing more community sport to resume in Launceston.

The Health Department is aiming to have the new clinic established at Inveresk within a fortnight, after which the Elphin Sports Centre committee can further plan for competitions to resume.

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Ms Courtney said the government was grateful for the Elphin Sports Centre's cooperation in having the clinic set up at the site at short notice.

"It was such an important time to be able to get testing set up in a drive-through capacity in Launceston for the community, and we've seen thousands of Northern Tasmanians tested through this facility," she said.

"We know how important sport is for Northern Tasmanians, and we know particularly basketball is close to the heart of many in the community, and so it's really exciting that we're working towards being able to have sport return here."

Even with no confirmed active coronavirus cases in Tasmania, the government is continuing to urge anyone with respiratory conditions, such as a runny nose or sore throat, to arrange to be tested via their GP - who can themselves carry out tests - or through the Public Health Hotline. Mobile clinics will also be operating at targeted regional locations.

A further 12 cases of coronavirus in Victoria on Monday indicated how far Tasmania had come compared with some mainland locations.

Ms Courtney said getting large numbers of negative tests would help Public Health officials in their decision-making as restrictions ease further.

"What we need to do, as we go forward and ease restrictions, it's really important that we continue to see several hundred tests a day across Tasmania," she said.

"We've seen really strong numbers, however it's really important that those high numbers of testing continue.

"We're going to continue our strategy of having fixed locations in the main areas such as Launceston, and this is going to be supplemented by our mobile clinics travelling to regional areas and also having pop-up clinics so that people can just turn up.

"As restrictions start to ease, and as the Premier and the government starts to consider things such as the border restrictions, we need to keep our testing numbers high."

Ms Courtney urged Tasmanians to continue adhering to social distancing guidelines, to wash hands regularly and to stay home from work or school if unwell.