The Lady Alexandra Victoria Alberta Edwina Louise Duff was born at East Sheen Lodge, Richmond, the elder daughter of Alexander Duff, 1st Duke of Fife (10 November 1849-12 January 1912), and Princess Louise, Duchess of Fife (20 February 1867-4 January 1931), the eldest daughter of the future King Edward VII and Queen Alexandra.
Lady Alexandra's father had been created Duke of Fife and Marquess of MacDuff in the peerage of the United Kingdom two days after his marriage to Princess Louise of Wales in 1889. When it became apparent that the couple were unlikely to have a son, Queen Victoria created him Duke of Fife and Earl of MacDuff in the peerage of the United Kingdom in 1900. The second dukedom of Fife had a special remainder in default of male issue to the Duke's daughters and their male descendants.
On 9 November 1905, King Edward VII created his eldest daughter Princess Royal. He also created granddaughters, Lady Alexandra Duff and Lady Maud Duff, Princess of Great Britain and Ireland with the style of Highness and precedence immediately following all members of the royal family styled Royal Highness. From that point, HH Princess Alexandra and HH Princess Maud no longer held their ranks from their father, but rather from the will of the Sovereign (their grandfather). Princess Alexandra succeeded her father as 2nd Duchess of Fife and Countess of MacDuff on 22 January 1912.
On 15 October 1913, the Duchess of Fife married her first cousin once-removed, Prince Arthur of Connaught, at the Chapel Royal, St. James's Palace in London. From that point until her death in 1959, she was generally referred to as HRH Princess Arthur of Connaught. Prince and Princess Arthur of Connaught had one son, HH Prince Alastair Arthur of Connaught, styled Earl of MacDuff (by courtsey) after November 1917.
During World War I, Princess Arthur of Connaught served as nurse at St. Mary's Hospital in Paddington. When Prince Arthur was appointed governor general of the Union of South Africa in 1920, she accompanied him to Pretoria and worked on behalf of local hospitals. Upon the couple's return to Britain, she continued to carry out royal duties. She died in her London home in 1959.
Her only son and the heir apparent to the dukedom of Fife, Alaistar Arthur, died in Ottawa in 1943, a year after succeeding his paternal grandfather as 2nd Duke of Connaught. When Princess Arthur of Connaught died, the dukedom of Fife passed to her nephew, James George Alexander Bannerman Carnegie, Lord Carnegie, the only son of her late sister Princess Maud, Countess of Southesk.