Lidia Thorpe takes new seat, figuratively and literally next to Senator David Pocock

Senator Thorpe took her new place, figuratively and literally sitting next to David Pocock after quitting the Greens party on Monday to "speak freely" on black sovereignty.

To her critics, those who would suggest she rode the coattails of the Greens and walks away with their six-year seat, she says they should "check themselves" for racism.

"If you're a true ally and you believe in Aboriginal people having a say in this country, then stop demonising me for the decisions that I'm making based on a grassroots collective of sovereign back people," the senator told the ABC on Tuesday.

READ ALSO: The Thorpe unshackling that had to happen

Parliament and the Australian Federal Police "failed to protect me" from far right and white terrorist groups, she said.

"I think I've copped enough even with whatever protection I've had."

As she walked into the chamber a freshly minted independent, Senator Thorpe's statement earrings proclaiming "Sovereignty Never Ceded", worn as she announced the split from the Greens, were gone. The message of her renewed purpose in the parliament having already carried across the nation in an explosive start to the political year.

There were no signs of acrimony the morning after both Senator Thorpe and the party she left behind made an effort to dampen any hint of ongoing tensions in their brief earlier remarks to the media on her departure.

At an earlier Greens party meeting on Tuesday, discussion was all business when it came to their now ex-colleague.

They pledged to work constructively with Senator Thorpe as they would any other crossbencher, leaving behind her bikie-relationship-hiding and other antics causing headaches for party leader Adam Bandt.

The Greens are now free to support the Voice to Parliament proposal as it appeared it was heading to do so from the start.

For her part, the senator has pledged only to support the Greens on climate policy.

Most of the Greens upper house members arrived early before the Senate's daily prayers - not an agenda item that Greens senators are generally enthused to attend - ensuring they were first in line to greet the new independent with visible fondness.

The independent was then mobbed by Senator David Pocock, her new (cross-) benchmate, and the senate leaders of the major parties, Nationals deputy leader Perin Davey, Liberal's Simon Birmingham and Labor's Penny Wong.

The new independent now has a key vote in the Senate, as one of the crossbenchers with whom the Labor government can choose to negotiate on contentious legislation.

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Where once Labor could have guaranteed her vote if it reached agreement with the Greens, now Senator Thorpe will be Anthony Albanese's concern rather than Mr Bandt's.

The government will now need two Senate crossbench votes in addition to the entire Greens contingent in order to pass legislation that the Coalition opposes.

It can choose from independent ACT senator David Pocock, Jacqui Lambie and her party colleague Tammy Tyrrell, Ralph Babet and the One Nation senators.

Labor pulled all the stops to show respect for Senator Pocock, with the Prime Minister personally entering the Senate to be present for his first speech, a gesture otherwise reserved only for new government senators.

With nearly a full six-year term to make her own power felt, expect she'll do that if not derailed by allegations of financial misconduct in her office - allegations she denies.

For that too, Senator Thorpe has an answer: "Which again is exemplary of the systemic racism and the state violence against black women particularly in this country."

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