The son of a Scottish medical doctor Jonathan Garner, who practised in Bath, Somerset (England), Arthur Garner was articled to theatre designer Charles J. Phipps after leaving school but eventually turned from architecture to theatre, first as a scenic artist (under the tutorage of George Gordon), and later as an actor and then manager. After touring the British provinces for a number of years he came to Australia in 1873 with his wife, actress Blanche Stammers, remaining in the country for some three years largely under the management of Harwood, Stewart, Hennings and Coppin.
Garner returned to Australia in 1879 as manager of the London Comedy Company, a troupe which included his wife, George Gordon and comic actor Fred Marshall. The following year he opened Garner's Theatre in Adelaide, a venture which brought him to the attention of J. C. Williamson and George Musgrove. The three men joined forces in November 1881 to lease theatres in Sydney and Melbourne, and the following year established the firm Williamson, Garner and Musgrove, also known as the "Triumvirate." The company's operations saw Williamson (the senior partner) handle the actors and various theatrical companies, Musgrove looked after the production side of its operations, and Garner organised its business affairs.
Although the firm was dissolved in 1890 following arguments between Williamson and Musgrove, those two men eventually put aside their disagreements and founded the new firm Williamson and Musgrove. Little is known of Arthur Garner's life or career after 1897, at which time he was declared insolvement in Melbourne.