Ollivier was a right-hand batsman. In February 1867, he became a representative cricketer at age 15, when he played for Canterbury against Otago at Hagley Oval; the first cricket game ever that was played on that ground. He was also playing when Canterbury first met Auckland in 1873; the year that the Auckland team was founded. He played against England in February 1877, and against Australia in January 1878. Injury forced Ollivier to retire from the game in 1883. He became a trainer, administrator and selector of players. In 1882, Edward Cephas John Stevens and Ollivier initiated the purchase of a parcel of land which became Lancaster Park; this was to overcome the problem of spectators not paying a fee at Hagley Oval. In 1893, he selected the New Zealand team for the match against New South Wales.
Mountaineering
Ollivier was known for his mountaineering exploits and Mount Ollivier is named for him.
Other sports
Ollivier was a noted sports person in rugby and athletics, especially sprinting. He was a successful chess player, was a founding member of the Canterbury Chess Club in 1877, and was dominion champion in 1888/89.
Professional career
Ollivier was an accountant by profession. His first employment was with D. Macpherson and Co.. His next position was with J. T. Ford and Co. He was in partnership with Trevor Grierson before becoming self-employed.
Community involvement
Ollivier was a member of many organisations, and he was often on the committee. He was president of the Old Boys' Association of Christ's College from 1895 until his death. He was deeply involved with the administration of cricket.
Ollivier was unwell for several months before his death. He went to Castle Hill in the high country for a change of air, but returned even more ill. He died at the early age of 46 on 21 October 1897 at home in the Christchurch suburb of Opawa. He was buried at Woolston Cemetery. It was Frederick Wilding's proposal that resulted in the Canterbury Cricket Association erecting the gravestone for Ollivier; the inscription reads "Erected by the Cricketers of New Zealand". He was buried on a Saturday, and out of respect to him, all cricket matches in Canterbury got cancelled on that day. Mount Ollivier near Aoraki / Mount Cook is named after Arthur Ollivier. In 1939, the peak was Edmund Hillary's first major climb. After Hillary's death in 2008, there was a proposal to rename the peak Mount Hillary as a memorial, a suggestion opposed by Arthur Ollivier's family.