Kathleen Mary Nunneley was born on 16 September 1872 at Little Bowden, Leicestershire, England, the daughter of John Alexander Nunneley, a wholesale grocer, and his wife, Kate Young. She began her tennis career at a young age, winning several championship events before she had turned 15. In 1891 she won the Brighton handicap singles title and in 1893 recorded victories in tournaments at Liverpool, Leicester, Nottingham, Northampton and Wellingborough. Although she never competed in the All England championship, Nunneley defeated the reigning Wimbledon champion, Blanche Hillyard. Her father committed suicide in 1893 and in 1894 she emigrated to New Zealand with her mother, three brothers and a sister, arriving on the Kaikoura at Wellington on 7 December.
Shortly after settling in central Wellington, Kathleen (known as Kate) Nunneley joined the Thorndon Lawn Tennis Club. In December 1895 she took part in her first New Zealand Lawn Tennis Association tournament. On winning both the ladies' singles and doubles titles, she was selected to represent New Zealand at the New South Wales championships in 1896, where she played with characteristic style to win both the ladies' championship and handicap singles titles.
Possessed of a powerful forehand drive and a keenly competitive spirit, Kate Nunneley did much to improve the standard of women's tennis in New Zealand. Despite being severely handicapped by the dress requirements of the day, she was an energetic competitor who enjoyed playing and practising regularly against men. She won 13 national singles titles – more than any other man or woman in the history of New Zealand tennis – in an unbroken run from 1895 to 1907. She also won 10 national doubles titles and nine national mixed doubles titles, twice with the champion player Anthony Wilding, and was a leading member of the New Zealand women's tennis team which made a triumphant tour of New South Wales in 1909.
By the time she visited England at the end of the First World War Nunneley had given up top-level competition, but tennis remained her ruling passion. Her generosity to the game was manifested by her decision to have the gold medals she had won at national tournaments made into a trophy for the New Zealand Lawn Tennis Association. This gift, the Nunneley Casket, was presented in 1928 and subsequently awarded each year to the winning team in the interprovincial women's tennis competition.
Away from tennis Kate Nunneley lived the life of an independent woman. She never married and for 30 years she enjoyed a successful career as a librarian, retiring from her position as assistant in charge of the reference department at the Wellington Public Library in 1935.
Continuing her love affair with tennis, Kate Nunneley returned to England to see the Wimbledon tennis tournament in both 1949 and 1953. Known for her charm, modesty and good sportsmanship, she was a popular figure. For her own remarkable achievements and her enthusiastic work with young players, she was made a life member of the Wellington and New Zealand lawn tennis associations. She was also a life member of her Thorndon club. She died in Wellington on 28 September 1956.