Yes, on occasion.
Princess Eugenie has undertaken limited public duties as her university studies took precedence. She often performs engagements connected with charities her mother supports, including the Teenage Cancer Trust. As a member of the British Royal Family, Princess Eugenie is frequently seen at important Royal events, such as the annual Trooping the Colour ceremony in London.
On 2 June 2011, Princess Eugenie visited the Royal National Orthopaedic Hospital with her father as one of her first official engagements. In April 2012 she signed on to be patron for the Hospital's Redevelopment Appeal; this was her first official patronage. In early 2013, Princess Eugenie with her sister Princess Beatrice visited Berlin and Hanover in Germany to undertake a series of engagements. These included representing the Queen at the reopening of the former Hanoverian royal palace, the Schloss Herrenhausen, on 18 January. It was bombed by the Royal Air Force during the Second World War.
Princess Beatrice has been present at a number of official Royal occasions, such as Trooping the Colour in London, and the Queen's eightieth birthday. She and her sister were also guests at the Concert for Diana, in memory of their late aunt organised by their cousins, Princes William and Harry. Both princesses attended the service of thanksgiving for Diana on 1 September 2007, representing their father, who was on an official visit to Malaysia. Beatrice was present at the wedding of her cousin Peter Phillips to Autumn Kelly in 2008, and the wedding of Prince William and Catherine Middleton. At the wedding, Beatrice's hat designed by Philip Treacy was remarked upon by some as an odd choice of fashion. Nonetheless, in May 2011, the hat was offered for sale on the internet auction site eBay with the proceeds going to charity: it was sold for £81,000 ($123,325), with the money split between Unicef and Children in Crisis. A few months later Princess Beatrice was seen at the wedding of her cousin Zara Phillips to Rugby player Mike Tindall.
Princess Beatrice performed her highest profile royal duties to date when she accompanied her grandmother, the Queen, to the traditional Royal Maundy services on 5 April 2012. Other than the Duke of Edinburgh, she was the sole member of the Royal Family to attend the Maundy Thursday services at York Minster with the Queen. There, Beatrice interacted with parishioners, received flowers from the public, and assisted the Queen as she passed out the official Maundy money to the pensioners. In the lead up to the 2012 Summer Olympics Princess Beatrice welcomed the Olympic flame on the steps of Harewood House near Leeds.
In November 2012, Princess Beatrice became the first royal patron of the York Musical Society.
In April 2013, Princess Beatrice became royal patron of The Helen Arkell Dyslexia Centre, a charity that she credits with helping her overcome her own academic challenges resulting from dyslexia.