One Nation leader Pauline Hanson said she will move the censure motion when the Senate sits next week, labelling Senator Thorpe as unfit to serve in parliament.
It was revealed on Thursday the Victorian senator didn't disclose a relationship with Dean Martin, the ex-president of the Rebels outlaw motorcycle gang, while she was sitting on a powerful parliamentary committee.
The ABC reported Senator Thorpe was in a relationship with Mr Martin in 2021 while serving on the law enforcement committee, which may have received confidential briefings about bikie gangs at the time.
Committee chair Helen Polley said a review was taking place to examine whether Senator Thorpe had been briefed on sensitive information about bikie gangs during the course of her relationship.
"There's been a breach of trust, and we want to check the facts," the Labor senator said.
"She has shown such poor judgement, declaring a conflict of interest is Senate 101 ... this feeds into the discourse that politicians are in it for themselves as the Albanese government is trying to restore that public faith in the integrity of politics."
Senator Polley said the committee will be advised of any breach next Tuesday, and members will be reminded of their duty to keep confidences.
"With Senator Thorpe's contempt for the Senate with the swearing-in ceremony and now the breach of trust in failing to advise of a conflict of interest, she should consider if it's the right place for her," she said.
While it is not known whether the censure motion will pass, Senator Hanson said the failure to disclose the relationship was a conflict of interest.
"The Greens demand integrity and principle from everyone except themselves," she said in a statement.
"If Senator Thorpe had principles she would resign from the Senate. If Greens leader Adam Bandt had integrity he would kick her out of his party."
The One Nation leader said she was exploring other sanctions or measures that parliament could take against Senator Thorpe in the wake of the revelations.
Following news of the relationship, Senator Thorpe resigned as the party's deputy leader in the Senate.
Mr Bandt said the lack of disclosure about the relationship represented a lack of judgement from the Victorian senator.
Senator Thorpe said she had accepted the mistakes she had made.
"I ... have not exercised good judgement," she said in a statement.
Education Minister Jason Clare said the relationship was a clear conflict of interest.
"You can't be on an inquiry investigating outlaw motorcycle gangs and be in a relationship with an (ex) outlaw motorcycle gang member, a bikie," he told Seven's Sunrise program on Friday.
"It seems to me just to be a no-brainer here that there is a massive conflict of interest."
Opposition Leader Peter Dutton said the Greens senator was unfit to sit in the parliament.
"Clearly she should resign, I think (Greens leader) Adam Bandt should do that. You can't receive briefings in the day and hang out in nice circumstances with the bikies. It doesn't add up," he told the Nine Network.
"It should be the first order of business for any corruption commission to look into that and probe into what might be leaked."
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