Farquhar was born in Cambridge, New Zealand, but spent most of his early years in Fiji. He was educated in New Zealand and began his university studies in Christchurch before completing his degree at Victoria University of Wellington, where he studied with Douglas Lilburn. He taught briefly at St Peter’s School in Cambridge before travelling to England, where he completed an MA at Cambridge University and also studied composition with Benjamin Frankel at the Guildhall School of Music in London. Upon his return to New Zealand he joined the staff of the Department of Music at Victoria University of Wellington (where he was appointed in 1976), retiring in 1993.
A committed advocate of New Zealand music, Farquhar was the Founder-President of the Composers Association of New Zealand (CANZ) in 1974, and from 1982-95 served on the Board of the New Zealand Composers Foundation, later. He was also a Trustee of the Centre for New Zealand Music.
Farquhar wrote numerous orchestral, choral, stage and instrumental works, along with songs and music for children. His reputation was initially established in the realm of music for theatre, notably with the incidental music for Anouilh’sRing Round the Moon(1953) and the operaA Unicorn for Christmas(1962) to a libretto by Ngaio Marsh, which enjoyed a royal performance during the Queen's 1963 visit to New Zealand.
In 1984 Farquhar was awarded the CANZ Citation for Services to New Zealand Music, and in 2004 he was made a Companion of the New Zealand Order of Merit for his services to music. Farquhar died in Wellington, New Zealand, on 8 May 2007.