Encore Theatre Company co-founder Belinda King said the team were "elated" to be able to lock in the new dates.

"I can tell you our cast, our orchestra, and our production team are over the moon," she said.

"We have been in a desert for the last 18 months and finally we are able to have a drink of water. We can't wait until October."

IN OTHER NEWS:

Ms King said following a round table discussion with director of Public Health Mark Veitch and members of government to navigate a way forward, herself and Tasmanian actor and producer John Xintavelonis were invited to meet with Premier Peter Gutwein and Arts Minister Elise Archer.

Ms Archer confirmed there had been constructive conversations between sector representatives, Public Health, and the government.

"We have been working hard to develop support measures that allow the live events and performing arts sector to get back on its feet and particularly assist our artists, theatre venues and producers to get back up and running in a COVID-19 environment," she said.

Ms King said the meeting was "very promising".

"We walked away from the meeting confident that we will see a number of improvements over the coming months, in line with directions from Public Health," she said.

Ms King said the Premier had asked for another meeting in mid-April to review current theatre arrangements.

The announcement of the show comes after the Princess Theatre was cleared for 75 per cent capacity audience numbers on March 22.

Mamma Mia will run from October 11-November 6 at the Princess Theatre.

Ticket details will be released soon.