As the minister now responsible for the National Capital Authority, Kristy McBain has also signaled she wants to work with the ACT government on its major infrastructure priorities - including a new sports stadium.

Ms McBain's promotion to the territories portfolio has been seen as a bonus for the ACT, given her electorate of Eden-Monaro surrounds the national capital and she has a pre-existing working relationship with Chief Minister Andrew Barr.

Anthony Albanese's election win has added significance for the two territories, as Labor had promised to prioritise debate on repealing the John Howard-era laws that ban them from legislating on voluntary assisted dying.

Independent David Pocock has vowed to introduce laws to repeal the so-called Andrews Bill in the first weeks of the new parliament if, as expected, he wins the ACT's second Senate seat.

Mr Pocock last week discussed territory rights during a meeting with Mr Barr and plans to hold talks with stakeholders in the coming days.

His enthusiasm could pressure Labor MPs to fast-track the timeline for their own legislation, allowing them to claim credit for the historic move.

Mr Pocock signalled he was ready to work with the new government to bring on a vote.

"I appreciate the new government will have a range of legislative priorities, however I believe there is broad support in the new parliament for restoring territory rights," he said.

"I believe it presents the new parliament with an opportunity to work collaboratively to right a longstanding inequality and demonstrate to the electorate that politics can be done differently."

In an interview with The Canberra Times after being sworn into the territories portfolio, Ms McBain couldn't guarantee a vote would be held in the first weeks of parliament's return.

But she was "really keen to make sure that we can proceed as quickly as possible". Either a private members or private senator's bill would be brought forward to repeal the ban, she said.

The first-time minister personally supports a repeal of the ban, a position based on her mother's experience working in the aged care sector.

Labor grants members a conscience vote on the issue, and half a dozen of its senators opposed lifting the ban when it was last debated in 2018.

The success of the Greens and so-called "teal" independents at last month's election will ensure the new parliament has a more progressive lean, increasing the prospects that a repeal of the Andrews Bill would pass both houses.

Ms McBain's portfolio also includes oversight of the National Capital Authority, which has attracted controversy over its handling of consultation on projects including the $500 million War Memorial upgrade.

The authority was last week subject to an scathing audit office report, which found it failed to show "value for money" after handing out more than $20 million in limited contracts.

The former Bega Valley Shire mayor has already signalled a desire to work with the ACT government on projects earmarked for Commonwealth land, including a potential new city sports stadium.

"I think the ACT can be absolutely assured that I am 100 per cent prepared to work with them and listen to them and, you know, see how we can collaborate on a range of things," she said.

"I'm not somebody that's going to remain aloof and outside their sphere of relevance."

Over the weekend, Mr Barr reiterated a new stadium wouldn't be built until the second half of the decade.

He suggested an upgrade to Canberra Stadium in Bruce remained a live option due to capacity constraints at the site proposed for a Civic venue.