Prince Andrew will replace Princess Anne on a forthcoming royal visit to southern Africa as she continues to recover from a chest infection.
The 66-year-old's illness was announced last week as her diary of immediate engagements was cleared on doctor's orders to allow her to recuperate at home.
A Buckingham Palace spokesperson confirmed she will now miss the trip to Botswana and Mozambique at the end of the month.
The Royal & Ancient Golf Club of St Andrews have named their first ever female members.
Princess Anne and six top female players are the now on the membership list after a 260-year history of only admitting men.
More than three quarters of the club's 2,400 members took part in a ballot, with 85 per cent voting to allow women members.
The club said in a statement on its website: "The Royal and Ancient Golf Club of St Andrews is delighted to announce that Her Royal Highness The Princess Royal, Dame Laura Davies, Renee Powell, Belle Robertson MBE, Lally Segard, Annika Sorenstam and Louise Suggs have accepted invitations to become honorary members of the club."
Badger Trust CEO Dominic Dyer told ITV News that Princess Anne is wrong to recommend the gassing of badgers.
"Princess Anne is fundamentally wrong," he said.
"Badger gassing does not work. It is very ineffective because you're pumping gas into a set with lots of tunnel entry and exit points.
"The gas does not disperse equally - it won't kill all the animals outright. On average 20-30% of them will die prolonged, long deaths or suffer brain damage as a consequence.
"So it's not effective and it also has huge humaneness issues associated with it as well."
Princess Anne has explained why she supports genetically modified crops - despite her brother Charles being an outspoken opponent of them.
"They do add to our ability to perhaps be more efficient users of the land," she told BBC One's Countryfile.
"I think in the long-term, when you've got the prospect of nine billion [people] to feed, you are going to need some help in doing that."
Prince Charles once warned that the development of GM crops risked creating "the biggest disaster environmentally of all time" and accused multinational corporations of conducting an experiment with nature which had gone "seriously wrong".
Princess Anne has suggested that Britain should eat more horsemeat to stop surplus animals being abandoned and said she thinks the food tastes "very good."
"An awful lot of the abandonments is because they don't perceive there to be any value in the animals," she told BBC One's Countryfile.
"The meat trade adds value to the animal so there is some point in keeping it healthy if it's got an end point that it can go to."
Asked if she had ever eaten horse meat, she replied: "Oh, certainly."
She described the meat as tasting "very good, actually."
Princess Anne has said that gassing badgers would be the most humane way to cull the animals.
The Government is considering introducing gassing after a report said that shooting badgers would not bring their numbers down enough to stop them spreading tuberculosis in cattle.
"Most of the people who did it in the past will tell you that gas is a much nicer way of doing it, if that's not a silly expression," she told BBC One's Countryfile.
"How it works is that you go to sleep, basically."
The royal owns a heard of around 30 cattle and has lost 15 rare white park cows to bovine tuberculosis in the last two years.
Gassing badgers is "the most humane way" to control their numbers, Princess Anne has said.
The Government is considering introducing gassing after a report said that shooting the animals would not bring their numbers down enough to stop them spreading tuberculosis in cattle.
"If we want to control badgers, the most humane way of doing it is to gas them," the Princess Royal told the BBC's Countryfile programme.
Campaigners have backed the Princess Royal for challenging the development of large-scale new towns and instead highlighting the benefits of limited expansion of rural villages.
The Campaign to Protect Rural England welcomed her intervention, saying it was important to have a "living countryside" with villages which grew "organically".