The South West Launceston branch of the party, which has about 40 members, unanimously passed the motion last week which included calling on Labor to release the full report carried out by Barbara Deegan into Mr O'Byrne's sexual harassment conduct.

Branch secretary Justin Harding said it was their belief that Mr O'Byrne had suffered enough and was entitled to a position in caucus.

"Whatever sins David may or may not have committed, he has been amply chastised and we think that calls for him to be basically expelled from Parliament are excessive," he said.

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"There is no question that he has suffered in terms of his career. There's a question of whether the punishment fits the crime or not. I think having lost the leadership, not having a portfolio, on the backbench, that further punishment is not appropriate.

"The rules, as they stand, the process has been fulfilled. He was found not to have breached party rules. There has to be some nuance involved, you can't just have a hanging offence for everything."

The Labor branch - one of four in Launceston, with a majority from an "older demographic" - was the latest to take a position on the matter after the Derwent Valley branch this week passed a motion calling on Mr O'Byrne to resign from Parliament.

Former Labor premiers Lara Giddings and Paul Lennon also called for his resignation, while Tasmanian Young Labor last month passed a motion that would effectively remove Mr Lennon from positions in the party due to his role as a private lobbyist.

The former premiers' view was shared by current leader Ms White, who reiterated the view this week after speaking about the experiences of Alysha, whose State Service sexual harassment complaint was claimed to have been mishandled.

Ms White said the Deegan report found - and Mr O'Byrne accepted - that his conduct was "unacceptable" and "wrong".

"I'm on the public record stating very clearly that I think that David O'Byrne should resign from the Parliament. I haven't changed my view on that," she said.

Tasmanian Labor is undertaking a review of its governance and party rules.

Ms White said she was looking to the mainland for best-practice guidance.

"I've also spoken with the national secretary of the Labor party to understand what work is happening across the country when it comes to ensuring there are best-practice policies in place around complaints handling, misconduct, sexual harassment across the Labor organisation," she said.

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"I have already made those calls, that work is underway. The review that will be handed down into governance and rules, I think, will make significant improvements to the way the Labor Party performs in this state."

When asked about the varying views within the party on the O'Byrne matter - including from high profile female members - Ms White said there were long-standing relationships.

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"You have to understand that the Labor Party is like a big family, and there are relationships that exist that are very personal based on very long-term interactions," she said.

"And in fact there are members of the Labor party who are family. There's always going to be loyalty there to one another.

"But that doesn't mean that the party as an organisation is abrogated from its responsibility to maintain a safe workplace and uphold appropriate standards."

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