Northern Territory Senator Jacinta Nampijinpa Price's defection to the Liberals has seemingly cost her a shadow cabinet position, with Senator Kerrynne Liddle promoted by new Liberal leader Sussan Ley.

Ms Ley found no room for Senator Price in her newly announced opposition frontbench, with Senator Liddle, an Arrernte woman, becoming the Shadow Minister for Indigenous Australians.

Senator Price, who sensationally moved from the National Party room to the Liberal Party room in the wake of the election - much to the chagrin of her former Nationals colleagues - will take the role of Shadow Minister for Defence Industry and Shadow Minister for Defence Personnel.

The role was previously held by Luke Howarth in the shadow outer ministry, with Senator Price previously the Shadow Minister for Indigenous Australians - a shadow cabinet position.

Asked about Senator Price's appointment and why she hadn't been appointed to the shadow cabinet, Ms Ley said she had spoken to the NT Senator who was "excited" to take up her new role, but denied it was a demotion.

"I'm delighted that Jacinta is taking up what is a really vital role, and her style of communication and relationship with Australian people will be incredibly valuable," Ms Ley said.

Senator Liddle, the first Indigenous federal member of parliament from South Australia, will take over the role of holding Labor to account in the Indigenous affairs portfolio. She was previously in the outer shadow ministry as Shadow Minister for Child Protection and the Prevention of Family Violence.

In response to the widening Closing the Gap metrics earlier this year, Senator Liddle asked why the government continued to "invest significant new money into Closing the Gap initiatives at the same time it is failing to make progress in key areas to actually Close the Gap".

"It cannot just blame the states and territories but should also look at those who manage the decisions that inform the initiatives," she said.

"The Government must also come clean about which Indigenous programs it will cut in order to fund its new measures."

She has also advocated for the reintroduction of the Cashless Debit Card (CDC), which was removed by Labor. Its withdrawal was welcomed by many, however issues surrounding people purchasing alcohol and gambling have been reported, causing some to call for its reinstatement.

"I can tell you, I've been approached by many people who were cheering the end of that card who now say to me: 'Kerrynne, what can we do to get the card back into communities?'" Senator Liddle said last year.

After abandoning her bid to become deputy leader of the Liberal Party in partnership with Angus Taylor - who lost the leadership ballot to Sussan Ley by four votes - earlier this month, Senator Price claimed she had broad support from the public to be Prime Minister.

"I know there's a lot of Australians who'd love to see that," she said.

Senator Price was highly critical of the Labor Party's approach to Indigenous affairs last term, rejecting calls to fully adopt an Indigenous-led approach to helping Close the Gap - as endorsed by the Productivity Commission.

She regularly advocated for an audit of all Indigenous programmes and called for a Royal Commission into sexual abuse in remote communities, despite Indigenous organisations calling it expensive political point scoring and arguing solutions were already at hand.

Senator Price also argued bureaucracy is suffocating Indigenous development and "box tickers" are contributing to the gap not closing, as well as siding with Pauline Hanson, despite the controversial Queensland Senator's years of racially-charged comments culminating in last year being found guilty of breaching the Racial Discrimination Act.

Despite being criticised by Indigenous groups, Senator Price has broad support from conservatives - including former PM Tony Abbott - who had called on her to have a larger role during the election campaign after being front and centre during the Voice debate.

The Saturday Paper reported Mr Abbott was a major factor in Senator Price's defection, having pushed his case to his former parliamentary colleague and now president of the Northern Territory's Country Liberal Party, Natasha Griggs.

Senator Price was critical of being "sidelined" during the election campaign and hit out at media reporting after she said the Coalition would "Make Australia Great Again" at a gathering in Perth before photos surfaced of her wearing a Donald Trump 'MAGA' hat.

Earlier this week, it was reported the Warlpiri/Celtic woman had been offered the chance to run for the Liberal Party in this year's election, with claims Peter Dutton tried to lure her to enter the race as a Liberal in either Lingiari or Solomon.

Both seats were retained by Labor, with Lingiari - which encompasses Alice Springs, where Senator Price resides - seeing a large swing towards the incumbent Marion Scrymgour.

In a statement addressing the claims, Senator Price told Sky News she had previously run for the lower house seat in Lingiari at the 2019 election.

"I did receive suggestions from various individuals, including supporters, colleagues and friends, who would have liked me to run for a lower house seat," she said.

"I remain content with that decision and look forward to (continuing) a big task that lies ahead for the Liberal Party in holding the Albanese government to account in the Senate."