Ardern will help open the summit with former New York City Mayor Michael Bloomberg.
It is "Climate Week" in New York City and climate change is firmly on the United Nations' agenda. But Clark warned New Zealand had to be seen taking action, rather than just talking tough on the issue to other countries.
"It's more convincing if you're making major strides yourself and New Zealand's been very behind on Nationally Determined Contributions - because we've had 'off on, off on, off on'," Clark said. Nationally Determined Contributions are emissions reduction targets set under the Paris agreement.
"It's taken forever and we're really behind. We're talking the talk, but people need to see that we're stepping up," Clark said.
Agricultural emissions in particular were a problem, Clark said, as other countries were aware that New Zealand was doing very little to reduce those emissions despite them making up about half of New Zealand's total emissions profile.
Clark attended leaders week in 2000 as prime minister, and was present during her time as the leader of the United Nations Development Programme, UNDP between 2009 and 2017.
Clark said it was an "incredibly busy week", but one that provided an incredible opportunity to bump into other leaders.
"Normally the Secretary-General would host a leaders lunch. That's a good opportunity to see upwards of 150 people at leader level."
Clark believed there was something about the cloistered UN complex that engendered these impromptu meetings.
"The UN precinct is off limits to anyone who doesn't have a special kind of pass. It's very tight. Behind the cordon area there is scope for leaders to rub shoulders and talk in the corridors," she said.
Clark said the other big opportunity for leaders to mingle was on the floor of the General Assembly hall itself.
Climate change colours the big international story to watch at the United Nations too, which is the breakdown in the relationship between the United States and China, alongside the fallout from the war in Ukraine.
Last month, China decided to halt climate talks with the United States in retaliation against Speaker Nancy Pelosi's visit to Taiwan, a self-governing island that China claims as its own.
Clark said the decision to halt talks was "disastrous".
She said the problem in the relationship was that the two countries could not agree on how to get along, with the United States wanting to limit cooperation to a handful of issues, while China wanted to work on improving the relationship overall.
"The US wants cooperation with China on areas it wants to prioritise like climate change and also a more effective pandemic prevention and response architecture.
"But the Chinese are saying 'you can't cherry pick the issues you cooperate over'."
Clark is herself a feature of the week. She will be moderating a panel on leadership during a pandemic. Her guests include Ardern, who will talk about New Zealand's Covid response and Ellen Johnson Sirleaf, who was president of Liberia during the Ebola crisis.
Another issue that has risen to the top of New Zealand's agenda at the United Nations is nuclear disarmament. Ardern raised the issue at the Nato leaders summit in Madrid earlier this year and disarmament minister Phil Twyford was in New York earlier trying to get states to step up non-proliferation efforts under an existing UN treaty.
The outcome of those talks was blocked by Russia in what Twyford called "an act of diplomatic sabotage".
Ardern told TVNZ's Breakfast on Monday that disarmament issues were "still a key topic close to our heart".
