"So I understand very much the issues for transgender people, and the need to have access to surgery and to counselling and drugs and support. We are very supportive of that in our policy."
King separated from her first husband, with whom she has a daughter, and has since remarried. She is retiring from politics after the election.
In her valedictory speech this month, King spoke about highlights from her Parliamentary career, including homosexual law reform in 1986.
"I was told that I was going to lose my rural seat in the 1987 election if I voted for reform - I increased my majority," King said.
"I learned that you can only ever vote with your conscience. And there are many more reforms that are needed in this area, particularly for transgender people, who continue to be discriminated against," said King.
The Agender New Zealand support and lobby organisation this year labelled the decades-long wait time for gender reassignment surgery "horrendous".
Ardern was also asked at yesterday's meeting about Labour's plan to reduce suicide rates, and she said more mental health funding was needed for support such as school nurses.
But she also said students could lead a movement raising awareness of mental health issues, in a way similar to the Sadd (Students Against Driving Drunk) campaigns of her school days.
"We have just got to start talking about it, talking together about it.
"In my day, there was a big movement to stop the loss of life from drunk driving. And a big movement started in our schools. We started these chapters all across the country.
"I want to see that kind of support network in our schools when it comes to mental health. That same movement for change. Because you guys know your peer groups, you know what's going on with one another. So I think it probably needs to start there."
Before flying to Gisborne, Ardern launched Labour's education policy at Western Springs College in her Mt Albert electorate, and was also asked about mental health support.
She discussed suicide reduction targets and declared she wouldn't feel good until there were no suicides at all.