However, during her stage interview, and speaking to the Rotorua Daily Post afterwards, Clark praised Ardern for her focus on economic sectors and her partner Clarke Gayford for setting "a great example of co-parenting".
"When I first was elected as an MP in 1981 you had to search the floors of Parliament for a ladies bathroom, it had been a boys' club," she said.
She went on to become New Zealand's second female Prime Minister, the first to be elected, and now spends a lot of time working on gender diversity.
She said her gender played a role in missing out on the United Nations General Secretary role in 2016.
"Maybe it was never going to be possible, but you don't know that till you try and I've found in life that if you don't try you're never going to get anywhere.
"I didn't win that one, but frankly I don't think that was any fault of mine"
During her run for General Secretary the world was in a "very particular geopolitical situation" and at least four of the five great powers didn't want a leader with a strong personality, she said.
"I'm not known for being a shrinking violet, I will stand up on things if I think there's a principle that's been offended I will defend it and they're used to electing secretary generals that are quite accommodating."
"Where the gender factor comes in, there is still in parts of our world a perception that while strength is always admired in men, not everyone is used to having strong women."
She said a strong woman was a bit more threatening than a strong man would be.
"We used to agonise over why New Zealand has a lower GDP per capita than other countries we like to compare ourselves with and one of the obvious factors was that they had higher proportions of women in the workforce."
"All the international research shows all the companies which have a stronger representation of women on their boards and senior management, do better and it's precisely because they are attuned to what women as a consumer of goods and services want."
Clark said "it's not a glass ceiling women have to break through, just a thick layer of men in the middle and that's the challenge really."
"There's a lot of things we can do to bring women up the ranks, we don't want the women all on the bottom rung, or the Māori all on the bottom rung. You want to see that diversity represented up through the structure.
"A lot of women have lost the opportunity to pass through because of decisions that haven't been easy ones about family, so they're going out of the workforce at a critical time and they're not making their moves at the same time as the men are."
She said in a lot of ways New Zealand was ahead, with the gender pay gap at 9.2 per cent narrowing, but there was an exception to that - "our very high levels of domestic and family violence".
"That's something we need a profound reflection on as a society. We've got some issues to look in the mirror and really take the best advice we can on."
Clark also discussed the man she described as a global "disrupter", American President Donald Trump.
"Trump gets elected by speaking to a group that's been left behind during quite a radical economic transformation in the United States.
"Whether you like him or hate him, he's upended things."
She said we live in an era "where you just have to expect the unexpected".
"When you're planning, you need to put the wildest scenarios on the table, because anything is possible."
