"I believe in my lifetime," she told reporters on Monday. 

But Ardern is in no rush to make it happen. 

"I've been very clear that despite being a republican, I'm not of the view that in the here-and-now in my term of office, that this is something New Zealanders feel particularly strongly about.

"I don't know that I've had one person actually raise with me generally day-to-day the issue of becoming a republic. This Government has prioritised those issues that we do see as a priority. But I do still think there will be a time and a place; I just don't see it as now."

Ardern said there are "a lot of issues that would need to be resolved in terms of our constitutional arrangements to be able to move to that place". 

Dame Cindy wouldn't be drawn on the issue. 

"Clearly I accept the Queen as the head of state of the Commonwealth and I'm here to support her and I'm here to act in a role as the Governor-General to perform the duty which is around uniting the country."

The Governor-General acts as the Queen's representative in New Zealand, a ceremonial position often referred to as the de facto head of state. The Governor-General appoints and dismisses ministers, but only on the Prime Minister's advice. 

Each parliamentary term begins with the Governor-General summoning in the new Parliament. The role also includes hosting events at Government House in Wellington, travelling throughout New Zealand to open conferences, and attending services and commemorations.

Dame Patsy, the third woman in New Zealand to hold the role of Governor-General, was appointed in 2016 for a five-year term starting from September that year. Her term will end on September 28 and Dame Cindy will take over in October. 

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As the first wāhine Māori to hold the role, Dame Cindy said she was "genuinely humbled" by the Prime Minister's offer. 

"The role of Governor-General comes with the patronage of many organisations, working with children and young people particularly around their wellbeing, working in the areas of mental health, around innovation, and also around education, working with the homeless and people with high and complex needs. 

"These are all areas that I have both championed and worked on in the past and I think while we're still working through over the next few months what the strategic programme will be, you can expect that these will be themes of the work that I continue to do as the Governor-General of New Zealand."

As for how she would deal with a constitutional crisis, Dame Cindy said she would seek good advice. 

"I think we can be really pleased today that we have a solid constitution and a head of state and that it's very stable. Taking good advice is going to be the key to that and making sure that I'm well-informed. That will include advice on any tricky constitutional and legal and other areas."

Ardern spoke with Queen Elizabeth II last week to advise her about the appointment of Dame Cindy, whom Her Majesty described as "wholly suitable" for the role. 

"I wanted to ensure that in the role we had someone that brought integrity to the role, that had a mana and values that New Zealanders have respect for and could look to should any constitutional issues arise in New Zealand," Ardern said. 

"I wanted to make sure that I worked through a process and offered the role to someone that I hoped, of course, would take it."

Ardern said her conversation with the Queen also touched on condolences over the death of her late husband, Prince Philip the Duke of Edinburgh. 

Ardern said she shared with the Queen how "sorry" she was about the death of her life partner, and shared some insights from his service in Wellington, the correspondence she received and reflections delivered in Parliament. 

"Whilst the convention is that you don't share details of these phone calls, I'm sure Her Majesty wouldn't mind that I conveyed that she was genuinely moved by the amount of time New Zealand had spent reflecting on his contribution." 

Retired MP Peter Dunne wrote in March about the prospect of New Zealand becoming a republic. He said we should follow Ireland and have a non-executive head of state, a role that would be virtually identical role to that of our Governor-General.

"The concentration of the current process in the hands of the Prime Minister of the day, and the secrecy that attends that, would be neither adequate nor appropriate for the selection of the President of the Republic of New Zealand."