Clarke left the role after eight years, not long after her unsuccessful 2016 bid for the organisation's top job.
Ardern, New Zealand's third female PM, is also not long back at work after six weeks' maternity leave.
When the 37-year-old gave birth to her daughter Neve in June, she became the first New Zealand woman Prime Minister to give birth while in power, and the second ever in the world, after Prime Minister of Pakistan, Benazir Bhutto, who gave birth to her second child while in office in 1990.
The Herald yesterday announced that Ardern would Guest Edit the newspaper's special September 19 Suffrage anniversary edition.