A documentary playing in Australia this month provides a happy and timely reminder that before there was Jacinda Ardern, there was Helen Clark.

The extraordinary post-parliamentary career of the former New Zealand prime minister is the subject of My Year With Helen. In it, filmmaker Gaylene Preston tells a story of leadership, patriarchy, women and power as she follows Clark into one of world’s most secretive – and significant – power processes, the one to be elected secretary general of the UN.

Clark’s pursuit of the position in 2016 was well known, but the precise mechanisms of her defeat in the shadowy, secretive realm of geopolitical horse-trading less so. Clark describes the film documenting her campaign as “fly on the wall”, but the revelation of its story is just how many more walls its other subjects are willing to erect. “It’s a bit of a thriller,” Clark tells me in our interview. “It’s the equivalent of the House of Cards of the UN. Metaphorically, candidates are [killed].”

It’s an extraordinary story – even more so for continuing Clark’s already compelling personal narrative.

Brought up on a farm outside the Hobbitonesque North Island city of Hamilton, Clark studied politics and taught it even as she pursued it. She learned the lessons well; once elected to represent the Auckland electorate of Mount Albert, she held the seat for 28 years. Mount Albert is now represented by Jacinda Ardern.

After entering parliament Clark held an impressive succession of cabinet posts before pursing the Labour leadership. She lost one election to conservative Jim Bolger in 1996 before sweeping to victory against the National party rival who rolled him, Jenny Shipley, in 1999. Clark remained Labour leader and New Zealand PM for the next nine years.

It says everything that after electoral defeat by John Key in 2008, Clark still managed to be voted the Greatest Living New Zealander in a national media poll. It says even more that Key himself admitted she deserved it. When she resigned from parliament in 2009, it was hardly to a quiet retirement. It was to take up the post of administrator to the United Nations development programme, one of the most powerful positions in world politics. She remained in the position until last year.

Rumours that she was considering a run as the UN secretary general surfaced in the Guardian in 2014. “There will be interest in whether the UN will have a first woman because they’re looking like the last bastions, as it were,” she told her interviewer, without explicit commitment to the idea. “If there’s enough support for the style of leadership that I have, it will be interesting.”

Interesting it certainly became; Preston began trailing Clark in Botswana, where Clark was engaging a local government forum in her UN role. “A typical country visit,” Clark explains as if it may be the same for anyone, “I met the president, the key ministers, met with women – and went out to be engaged on some kind of mission.”

Yet the film finishes in Manhattan, where the documentary recorded the last six months of Clark’s campaign within a less accommodating environment. “I think that what does come out is the unreality of that bubble of life in New York,” Clark says of the process the film depicts, “which is governed by those who got their seats on the security council in 1945 before you and I were born.”

What discussions are and aren’t made available to the filmmakers allegorise the implicit tension within the campaign tale. One innovation of the 2016 process was that while nomination hearings were made in public before the general assembly, the security council pursued the official balloting in secret. “You have have 15 votes, you can’t be sure what the permanent members are doing,” explains Clark, “(but) the permanent members have a different coloured ballot paper for the permanent ballot paper … The veto card comes out and any one of the five permanent members can kill a candidate off.”

Despite inevitable leaks to journalists, there is, she says of the election, “Nothing transparent about it. Compare that to real life out there, real people, and the need they have of the UN for peace, security and development. And that’s quite a disconnect.”

Clark made it to fifth place in the sixth ballot before her own candidature was killed off. Watching the film, she suggests, one can make “an informed guess” as to who was responsible for that.

“I’ve been in public life for a long time, it goes with the territory,” she tells me, “you work out how much you want people to see, how much they can see, and what they can’t.” But ever the leader, ever the diplomat, ever the political intellect, Clark’s understanding of power remains expert, worldly and wry. “But a good filmmaker or reporter,” she says, “will work out what’s going on, without having to be told.”

• Sydneysiders can take part in a live Q&A with Helen Clark as well as watch her documentary, My Year with Helen, on 22 March at Event Cinemas George St Sydney. Pre-purchase tickets essential: demand.film