Princess Anne represented her mother, Queen Elizabeth II, when she visited Australia with her husband, Vice Admiral Sir Tim Laurence.
They were received by the Governor of New South Wales, Margaret Beazley, and her husband, Dennis Wilson.
According to Buckingham Palace, Princess Anne opened the Royal Sydney Easter Show on the first day of her visit.
The annual show is organized by the Royal Agricultural Society of New South Wales and brings together regional communities to showcase the best produce, livestock, crafts and skills.
The Princess Royal later met with street vendors at the event, where she learned more about the challenges facing those living on the land after years of recent drought and flooding, the palace said in a tweet.