Bishop was one of three contenders for Liberal leadership, after Turnbull was forced to step down, but was the lowest polling despite being the public favourite.
She resigned from cabinet on Sunday to sit on the back bench and new Prime Minister Scott Morrison, on Bishop's advice, has replaced her with former Defence Minister Marise Payne. There is speculation Bishop could become Australia's next Governor-General.
In other portfolios with a frequent interface with New Zealand, former Trade Minister Steve Ciobo resigned his post in support of the Dutton challenge and the new Trade Minister is Simon Birmingham, the former Education Minister. Christopher Pyne is the new Defence Minister.
Peters has not yet spoken to Marise Payne but he has an introductory call scheduled for Wednesday morning, before next week's Pacific Islands Forum in Nauru.
Morrison has decided not to attend the forum and Payne will be representing Australia.
They shared with me their concern about the external forces ... that are involved in those attempted spills in Vanuatu. It's a known fact.
Morrison's first overseas visit will be to Indonesia, to put the seal on a new free trade deal.
Peters said his visit to Vanuatu allowed him to meet local politicians who were concerned about the fact there was almost always a leadership spill in the year before an election.
"They shared with me their concern about the external forces, so to speak, that are involved in those attempted spills in Vanuatu. It's a known fact."
"It is sadly interference. It is not elements that are respecting Vanuatuan people's right to make these decision."
He would not say who constituted the external influence.
"They understand acutely that if they are to be successful they have got to stabilise their politics and not have governmental change in between elections, which is just too common in some parts of the Pacific."
The irony of what had happened in Australia was not lost on the Vanuatu politicians, he said.
National foreign affairs and trade spokesman Todd McClay said it was positive that Morrison's first trip, to Indonesia, was about trade, but he hoped Morrison's second trip would be to New Zealand.
McClay said Ciobo had been a good friend to New Zealand in trade and they had worked closely on the Pacific Alliance and on TPP after the United States withdrew.
"But ultimately there is institutional knowledge on both sides. Trade ministers may come and go but the free trade train needs to continue and I have faith that the Scott Morrison Government will continue to recognise we can do more together on the world stage than apart."
It would be important for Trade Minister David Parker to meet Birmingham quickly and work out the ways to work together.
There was a big challenge looming about the World Trade organisations dispute settlement system.
"It is friends of America like Australia and New Zealand that need to be talking to them directly to make sure the WTO is not irreversibly harmed."
