The British primatologist Dame Jane Goodall believes the Duke of Sussex will give up hunting because of his wife’s dislike for the sport, and thinks he has been finding life “a bit challenging” since the couple moved to North America.

Goodall, 86, a friend of the pair who has been a guest at their Frogmore Cottage home in Windsor, said in an interview with the Radio Times that Harry and his brother, the Duke of Cambridge, were champions of the natural world – “except they hunt and shoot”.

She added: “But I think Harry will stop because Meghan doesn’t like hunting, so I suspect that is over for him.”

The conservationist was speaking about her latest documentary, The Hope, on National Geographic and National Geographic Wild, marking the 50th anniversary of Earth Day. It includes footage, previously released, of her mimicking an intimate ape greeting with Harry.

Asked if she hoped he would remain a supporter and ally, Goodall said: “I don’t know how his career is going to map out, but yes, I’ve been in touch, though I think he’s finding life a bit challenging just now.”

Harry and William have faced criticism in the past over hunting. Both are opponents of the illegal wildlife trade and supporters of the campaign to protect endangered species.

Critics have condemned their participation in Sandringham Boxing Day shoots at the Queen’s Norfolk estates. In 2014, a 10-year-old photograph of Harry emerged showing him crouched over the body of a water buffalo he had shot dead during a hunting trip on his 2004 gap year in South America.

Dr Jane Goodall at the World Economic Forum in Davos, Switzerland, in February. Photograph: Alessandro della Valle/AP

Also in 2014, the brothers went on a deer and wild boar hunting trip in Spain a day before William launched a high-profile appeal to stop the illegal hunting of wildlife.

Goodall also spoke about environmental activism among the young. “It’s the youth that gives me the most hope,” she told the Radio Times. “I’m not particularly thrilled about children missing school and marching – I’d rather they did things like planting trees and clearing rubbish – but it’s a sign that young people are determined to have a voice.”

Goodall has a good relationship with Harry, who interviewed her for the special edition of British Vogue guest-edited by Meghan.

The primatologist also revealed that Harry “hinted” at his wish to leave the royal family months before the couple made their public announcement.

Recalling a comment he made on the subject during the Vogue interview, Goodall told the Daily Mail’s Weekend Magazine: “At the end [of the conversation], Meghan came in to listen with Archie. He was very tiny and very sleepy – not too pleased to be passed from his mummy. I think I was one of the first to cuddle him outside the family.

“I made Archie do the Queen’s wave, saying, ‘I suppose he’ll have to learn this.’ Harry said, ‘No, he’s not growing up like that.’”

During the Vogue interview, the two spoke of how unconscious bias can affect racism, saying that many people failed to acknowledge their own bias due to their upbringing and environment.