Lidia Thorpe's relationship with ex-bikie boss Dean Martin heightens calls for inquiry

Senator Thorpe was booted from the party's leadership team on Thursday, over revelations she dated former Rebels Victoria boss Dean Martin while sitting on the committee, which receives classified information on outlawed motorcycle gangs.

Prime Minister Anthony Albanese has backed growing calls for a probe into whether the relationship, which Senator Thorpe did not reveal to Greens leader Adam Bandt, was marred by conflicts of interest.

The Coalition is also leaving open the option of a censure motion in parliament next week, demanding Mr Bandt call for Senator Thorpe's resignation.

One committee member said the "absolute disgrace" may have "tainted" the committee in the eyes of law enforcement, charged with providing confidential briefings to members.

Joint committee on law enforcement chair and Labor senator Helen Polley on Friday described an investigation as an "appropriate course of action", insisting she would not pre-empt the outcome.

"This committee deals with highly classified and sensitive material in relation to security information. Therefore the integrity of the committee must be upheld at all times," she said in a statement.

"As the Prime Minister said yesterday, this isn't simply poor judgement ... these are serious matters of disclosure and potential conflicts of interest that deserve to be looked into."

Committee member and Liberal MP Jason Wood labelled Senator Thorpe's secrecy an "absolute disgrace", saying it may have long-term ramifications for its ability to operate.

Mr Wood told The Canberra Times her behaviour had "tainted" every member of the committee, past and present, which had previously operated in a serious, bipartisan manner.

"Being associated with a bikie? In the police force, you'd be getting sacked for that," he said.

"I can see police now saying, 'Why the hell are we going to go and brief this committee? We can't trust it'.

"Why would law enforcement now trust the committee? It's been burned by her not disclosing her connections with a bikie. Their main target on that committee is outlaw motorcycle gang members."

Mr Albanese demanded a "full explanation" from Mr Bandt, saying the Greens leader's lack of knowledge showed the party needed to revamp its procedures.

"We will examine any proposals should they be moved," he said.

"My understanding is that the committee of which the senator was a member is examining what details went before the committee to make sure that there has been no conflict there. It is appropriate that that action takes place."

Deputy Liberal leader Sussan Ley called for Senator Thorpe to face a censure motion, describing her as "unfit to remain in parliament".

But Ms Ley said whether the Coalition would refer the Greens senator to the powerful parliamentary privileges committee would be clearer next week.

"I'm calling on the Greens leader to ask Senator Thorpe to resign from the Parliament," she said.

"You can't get briefings from law enforcement agencies by day and be in bed with bikies at night."

In a resignation statement on Thursday, Senator Thorpe conceded she did "not exercise good judgement" by failing to disclose the relationship.

But she flatly rejected suggestions she had passed sensitive information to Mr Martin. Mr Bandt stressed no one had accused her of doing so. The Canberra Times does not suggest she mishandled confidential information.

Mr Wood, a former law enforcement officer, warned outlawed motorcycle gangs "do everything they can to get information".

He joined calls for the allegation, which he described as "one of the most serious" he had seen in Parliament, to be the subject of a probe.

"It may be completely innocent, with nothing ever discussed, or maybe not. The only way to find that out is having an inquiry where people are compelled to [speak]," he said.

"It has to be subject to an inquiry. The Greens are always the first ones to say that they're more pure than snow."

Independent senator for the ACT David Pocock said he was "shocked" by lax declaration requirements for politicians, saying he was often not obliged to declare his spouse's interests.

Senator Pocock described the revelations as "concerning", but was yet to form an opinion on whether an investigation was necessary.

"It's such a privilege to to be in there and represent your state or territory or your electorate. And with that privilege comes responsibilities," he said.

"It's something that I would like to see [prompt] the standard [to be] raised in the Parliament."

Mr Bandt stopped short of calling for Senator Thorpe to leave Parliament, keeping her as the party's spokesperson on First Nations issues and insisting she "has the potential to be a very good senator".

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"I've never, ever called for a member to resign from from Parliament from either side, but this is such a huge breach," Mr Wood said.

"I just cannot see any committee now would trust her."

Mr Martin's association with the Rebels spanned more than two decades, but he has no criminal convictions.