Tasmania's Opposition has accused the Premier of allowing one of his senior advisers who confessed to trolling people online to walk away with a "golden handshake".

In March, Will Hodgman told the media Martine Haley had resigned after the ABC revealed she had used a fake social media account in an attempt to get a woman sacked.

"Today I have accepted the resignation of Martine Haley, a senior adviser in my office," Mr Hodgman stated in a media statement on March 6.

The victim of Ms Haley's trolling was Angela Williamson, who is taking Cricket Australia to the Federal Court after she was sacked in June for writing a series of tweets criticising State Government policy, including on abortion.

But in Parliament on Wednesday, Mr Hodgman admitted that instead of her resignation being accepted, her contract was not renewed.

"Ms Haley was prepared to resign, offered her resignation, but her contract was not renewed," said Mr Hodgman.

If Ms Haley's resignation had been accepted she would not have been eligible for the $45,000 payout.

Labor Leader Rebecca White asked Mr Hodgman why he said Martine Haley had resigned.

"That would have meant she would have left with only her leave entitlements, not her significant payout at the taxpayers' expense," she told Parliament.

"You've given her a golden handshake," Deputy Opposition Leader Michelle O'Byrne shouted at Mr Hodgman.

"It is not up to me to determine what their entitlements are," Mr Hodgman replied.

Angela Williamson was sacked by Cricket Australia because of tweets criticising Tasmanian government policy. ( Twitter: Peter Mathew )

Hodgman grilled on sacking saga role

Premier Will Hodgman also faced a barrage of questions from the Opposition about his and Health Minister Michael Ferguson's involvement in the Angela Williamson matter.

Ms White asked Mr Hodgman whether he had a meeting with Ms Williamson while she still worked at Cricket Tasmania during which she told him about her abortion.

"The answer is yes," he said.

Ms White also asked if Mr Hodgman had been in contact with Cricket Tasmania about Angela Williamson prior to her sacking in June.

He did not address the specific question:

"I certainly have not sought to pressure or complain or anyway influence Angela Williamson's employment with Cricket Tasmania or Cricket Australia," he said.

Ms White asked Mr Hodgman if he had a conversation with a Cricket Tasmania board member at the Ricky Ponting Medal dinner about Angela Williamson "where it was indicated her relationship with government was broken".

Mr Hodgman said the question was a "conspiracy theory that was entirely unfounded".

He said the Government had regular contact with Cricket Tasmania and again stated the Government had not sought to influence Ms Williamson's employment.

'Payout condones bad behaviour', says Labor leader

Ms White said awarding a payout to a disgraced staff member signalled the behaviour was condoned.

"That sends a terrible message to the people of Tasmania about the standards this government is willing to accept," she said.

"The Premier should have accepted the resignation and not provided a $45,000 handout to a member of staff who acted completely inappropriately."

The Hodgman Liberal Government did not hold a press conference on Wednesday despite requests from media to address questions regarding Ms Haley.