Arthur O'Leary (15 March 1834 – 11 March 1919) was an Irish composer, pianist and teacher.
O'Leary was born in Tralee, County Kerry, both his father (also named Arthur) and uncle Daniel having been talented musicians, too. Arthur Senior was said to be first cousin to Arthur Sullivan's grandfather in an obituary for O'Leary written by W. H. Grattan Flood. When young Arthur's talents were discovered at the age of ten, a visiting barrister, Wyndham Goold became his patron: in May 1844 he sent him to school in Dublin and secured private piano tuition. With financial backing from others, including John Stanford (father of Charles Villiers Stanford), and with letters of introduction from William Sterndale Bennett, O'Leary was able to study at the conservatory in Leipzig, where he arrived in 1847 to study piano (with Ignaz Moscheles), organ, violin, and harmony (with Julius Rietz). During this time he was invited several times to musical dinners where he met, besides Moscheles, Felix Mendelssohn-Bartholdy and Joseph Joachim. He also attended Mendelssohn's funeral in 1847.
Between February 1852 and December 1854 O'Leary studied the piano with Cipriani Potter and Sterndale Bennett at the Royal Academy of Music (RAM), London. He became an assistant professor at the RAM in 1856 and elected a fellow in 1864, teaching piano and composition. Among his more notable pupils were Alicia Adelaide Needham, Charles Villiers Stanford, and Arthur Sullivan. He also had other teaching positions in London at institutions including the National Training School for Music (from 1876), the Guildhall School (1880–1900), the Crystal Palace School of Science and Art (from 1886), and the Beckenham School of Music (from 1894). He resigned from the RAM and other positions in 1903. He was elected a member of the Philharmonic Society in 1875.