Lara Alexander says she won't commit to premier's new deal

Meanwhile, fellow independent John Tucker says he will take time to consider the premier's demands.

The premier wrote to Mrs Alexander and Mr Tucker, both former Liberal backbenchers, on Thursday night following a meeting with the pair.

In separate letters, he expressed concerns about threats made by Mr Tucker last month that he would consider withdrawing confidence in the government should the government progress with its southern high-performance training centre for a Tasmanian AFL team and if his animal welfare demands were not met.

Under a new agreement, the pair must commit to confidence and supply in the government. They would not be able to support bills, bill amendments, or motions from Labor, the Greens, or other independents unless the government agrees.

The pair would, however, be able to bring forward their own motions and bill amendments.

"If we are unable to reach a new agreement before the resumption of parliament on 5 March 2024, I will be forced to consider all options, including potentially advising the governor to dissolve the house," Mr Rockliff wrote.

Mrs Alexander said she could not support one particular term of the new agreement, which would restrict herself and Mr Tucker from supporting bills, bill amendments and motions from non-government parliamentarians.

"What it does, in effect, is that it makes us less effective than a backbench because at least with backbench and with members of the Liberal government, you can actually cross the floor and have a vote of conscience," she said.

Mrs Alexander said she believed a renegotiated agreement was orchestrated to shut down her freedom to act independently in parliament and essentially trigger an early election.

"The reason I became an independent was around the principles of transparency, freedom of speech and the capacity to engage in good solid conversations and have differences of opinion," she said.

"This is designed just to block all that."

Mrs Alexander said she had upheld her promise not to block supply, pass the last state budget and maintain confidence in the government.

She said the only time she considered withdrawing confidence was following Mr Rockliff's stouch with former attorney-general Elise Archer, who was asked to resign from cabinet after a derogatory text message about victim-survivors was leaked.

Ms Archer announced she would resign from parliament, only to change her mind a day later and say she would sit on the crossbench as an independent.

The premier, too, gave her an ultimatum to either commit to confidence and supply in the government or he would call an election.

She resigned hours after the ultimatum was issued.

"This is a bit like Elise Archer 2.0 for me," Mrs Alexander said.