Stalking deer is a historic practice in the Scottish Highlands and designed to control the population of deer (which have no natural predators in the UK).
According to Express, a spokesman for the League Against Cruel Sports said, "Killing deer for a sport is a horrible pastime. It's very sad that she has chosen to participate in this cruel sport.
"It's hardly setting a good role model for young women, killing animals and I can't see that this will do her reputation any good whatsoever.”
PETA's Yvvone Taylor also compared the Duchess to Princess Diana, pointing out that the late-Princess of Wales took a stance against hunting.
"Some have compared Kate to Diana, but Diana never wore fur and she also turned against blood sports."
In the weeks leading up to their royal wedding, Diana was criticised for injuring a stag while hunting with the Prince of Wales.
Although Diana was "blooded" by ghillies – a ceremony which involves a hunter's forehead being smeared with the blood of their first kill – she vowed never to take part again.
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The Duke and Duchess of Cambridge will be visiting the Queen's estate in Balmoral with their children Prince George, Princess Charlotte and Prince Louis over Britain's summer.
However, royal expert Robert Jobson told the Daily Mail that William and Kate are waiting until Prince Harry and Meghan Markle return to Windsor before heading up to Balmoral, due to reports of tension between the Cambridge and Sussex royals.