The election of Australia's new prime minister means there's an opportunity for changes in the trans-Tasman relationship.

It's already got off to a good start. Anthony Albanese kept the Labor faithful waiting on Saturday night, because he was taking a phone call from Jacinda Ardern.

The prime minister says she called Australia's new prime minister-elect as he was preparing to address his supporters.

"It was a warm conversation and I'm really looking forward to formally meeting with him soon," she said in a statement.

"Australia is our most important partner, our only official ally and single economic market relationship, and I believe our countries will work even more closely together in these tumultuous times."

New Zealand and Australia might be mates but the relationship has taken a frosty turn of late, over Australia's501 deportation policy.

"I've been absolutely clear, this is corrosive to our relationship," said Ardern in 2020.

She was standing right next to a grinning Scott Morrison, and taking him to task over the policy.

"We have a simple request: send back Kiwis, genuine Kiwis. Do not deport your people, and your problems," she said.

501 advocate Filipa Payne said the Morrison government used deportees as a political football.

"Any time they want to get any community support, they'd amend the legislation.

"I pray Labor comes in and amends it so that it can now be implemented with fairness, with humanity, and with respect and dignity for people that it's impacting on."

Payne said Australia was not our closest ally at all.

"No, I think they were our closest enemy. Australia is damaging our country daily, we just have to look at the lack of support that deportees are getting in New Zealand, what it's doing on our society, but also the brutality that Australia implements in those detention centres is causing global damage."

Morrison was preparing to introduce new legislation to strengthen the so-called 'character test,' making it harder for deportees to appeal.

The bill was passed in Australia's lower house, with Labor's support. But the Australian Senate didn't have a chance to debate it before the election was called, and now Morrison is out.

Payne believes Albanese's win is promising, and has high hopes and expectations.

But there is little sign yet that he will end the policy, or relist the bill.

"Section 501 applies for breaches of people who are on visas, and if people commit serious offences then action should be taken in Australia's national interests," Albanese said earlier this month.

And then there's AUKUS. New Zealand was left out of the new security partnership between Australia, the UK, and the US last year.

ACT's foreign policy spokesperson Brooke van Velden said a new leader is an opportunity to strengthen our ties when it comes to defence.

"New Zealand needs to play its part in the Pacific too. Our hope as the ACT party is that this new government in Australia will be a reset for our relationship.

"We really need to work together to show we are committed to peace and security in the Pacific."

It's not just Australian Labor toasting success.

The Australian Greens had their best-ever election result, and could hold the balance of power in the Senate.

Greens co-leader James Shaw said his Aussie counterparts finally have a chance to use their voice.

"It's absolutely critical. The Australian Green Party has been very, very strong in leading on climate change, they just haven't been in a position to be able to exert influence over a government until now."

How much influence they will have is unclear. Albanese has pledged to make Australia a renewable energy superpower, but also supports new coal mines.

Last week the New Zealand government revealed its Emissions Reduction Plan. Shaw said there is an opportunity for us to share our experience.

"I think what we can do is work with the Australians and say 'look, here's been our recent experience and that seems to be gaining some momentum and some traction now, are there things we might be able to share that get us both on the same page?'"

A wishlist for Australia's new leader, from its neighbour.