"New Zealand was the first self-governing country in the world where women won the vote and that's an enormous source of pride."
While Benazir Bhutto was the first female leader to give birth in office, she had had to "slightly hide the fact she was preganant and get on with it".
Ardern had done it openly and she and her partner were very consciously role-modelling.
"You can do things how you want and I think that's very very valuable."
Clarke, who has been in her post for six months, has three young children with New Zealand husband Toby Fisher.
She was on Stewart Island with the Stewart Island Women's Forum at an event to mark 125 years of women's suffrage in New Zealand when the news came through last Thursday.
Theresa May greets Jacinda Ardern outside No 10 in April this year when Ardern was attending the Commonwealth Heads of Government Meeting. Photo / Supplied
"We all toasted the arrival and I think it is a wonderful thing actually in the year that we are celebrating 125 years of suffrage in New Zealand that a sitting prime minister can have a baby and that she and Clarke Gayford are both role-modelling that for people around the world."