Primrose was born in Glasgow on August 23, 1904, to John and Margaret-McInnis Primrose, and had two younger siblings. His first musical instruction began in 1908 with violin lessons from Camillo Ritter, who was a former student of Joseph Joachim and Otakar Sevcik. At the young age of 12, Primrose made his debut as a violinist performing Mendelssohn's Violin Concerto at St. Andrew's Hall in Glasgow. In 1919, he moved with his family to London and began studying at the Guildhall School of Music. He graduated in 1924 with honors, but later admitted that his courses were not very challenging and that he never applied himself. Two years later, at the suggestion of his friend and accompanist Ivor Newton, Primrose began studying with Eugène Ysaÿe in Belgium. Since he was young, Primrose preferred the darker sound of the viola to that of the violin, but his father insisted that he play the violin. When Ysaÿe discovered Primrose's love for the viola, he encouraged his student to pursue it instead of the violin. This change, paired with Ysaÿe's mentoring, helped Primrose achieve a new level of refinement and musicality.
His first professional experience as a violist began in 1930, when he joined the London String Quartet. He toured extensively with the group until it disbanded in 1935 because of complications related to the Great Depression. In 1937, Primrose joined the newly formed NBC Symphony led by Arturo Toscanini. Although he never held the position of principal violist, he enjoyed four years with the orchestra, and he also formed the Primrose Quartet in 1939. In this capacity, he stayed very busy rehearsing and performing until he left the orchestra in 1941 to pursue a career as a soloist. He toured with Richard Crooks throughout Europe and the Americas, and in 1943 he started working with concert manager Arthur Judson and performed with many of the leading conductors and orchestras of the time. The violist also performed chamber music with the Heifetz/Primrose/Feuermann Trio and the Schnabel/Szigeti/Primrose/Fournier Piano Quartet.
Primrose was an advocate for new music, and several composers wrote specifically for him including Milhaud, Britten, Rubbra, and Bartók, whose commissioned viola concerto is one of the most well-known. In 1946, Primrose began to develop a hearing problem that eventually left him unable to hear specific pitches; however, he kept touring and recording throughout the 1950s. He formed the Aspen Music Festival Quartet in 1954, and collaborated in the Heifetz-Piatigorsky chamber music series. His declining hearing coupled with a heart attack that he suffered in 1963 led him to shift his career from performing to teaching.
Two years later, Primrose began his first educational appointment at Indiana University, and in 1972 he taught at the Tokyo National University of Fine Arts and Music. He also became associated with other schools in Japan, including the Toho Gakuen School and the Suzuki Institute in Matsumoto. In the late '70s, he edited and arranged music for the viola and he published his memoirs, Walk on the North Side. From 1979 until his death in 1982, he taught at the Brigham Young University, where he established the William Primrose International Viola Archive within the Harold B. Lee Library. ~ RJ Lambert, Rovi