Arthur Hadfield Fisher was born at Nelson, New Zealand, on 11 February 1871, the son of Thomas Richard Fisher, a merchant, and his second wife, Frances Anne Hadfield. Thomas Fisher joined the Standard Fire and Marine Insurance Company in 1877 and the family moved to Christchurch. In 1881 he was appointed general manager in Dunedin. From 1881 to 1885 Arthur Fisher attended Otago Boys' High School, and from 1886 to 1887 Waitaki High School, Oamaru, where he excelled at sports. He received a special cap for good play at rugby throughout the season, and in 1887 was athletic champion.
On his return to Dunedin late in 1887 Fisher joined the Carisbrook Cricket Club, then synonymous with the professional class of the city. Throughout the 1890s and early 1900s he was the leading member of the club's senior A team, assisting it to 12 championship wins in the Dunedin senior cricket competition.
Fisher made his first-class début for Otago against Canterbury in January 1891. For the next 20 years he and off-spinner Alex Downes formed one of the most formidable bowling partnerships ever seen in New Zealand cricket. Fisher appeared in 40 first-class matches for Otago, taking 176 wickets at a cost of 15.71 runs each. A left-arm medium-fast bowler, his stock ball was the in-swinger, but he could break the ball from leg as well as bowl the yorker. He always kept an excellent length and unsettled the batsman by varying his pace. Fisher was also a useful aggressive right-hand batsman, and a brilliant fielder at cover or point.
In the 1896–97 season Arthur Fisher was at the height of his powers. In November 1896 he and Downes skittled Canterbury on a soft Carisbrook wicket for totals of 27 and 49. Later in the month he destroyed the strong 1896 Australian eleven, capturing 11 wickets for 78 runs for the Otago fifteen. In January 1897 Fisher took nine wickets for 50 runs in an innings against the touring Queensland team – still the best figures for an Otago bowler. He finished the season by taking seven wickets for 11 runs in the return match against Canterbury on Lancaster Park. These performances saw him chosen by the New Zealand Cricketers' Annual as bowler of the season.
Fisher was invited to play in Australia in 1897 with a view to representing that country against the visiting English team. Unfortunately a delayed departure from Dunedin and severe seasickness did not help his cause. He met with limited success and little attention in Melbourne club cricket and was regarded by some as overrated and only good on the soft New Zealand wickets. He returned to Dunedin early in 1898 and later in the year began a five-year period as club captain of the Carisbrook Cricket Club.
Arthur Fisher played five matches for New Zealand between 1895–96 and 1906–7. He was a member of the inaugural New Zealand team to visit Australia in 1898–99; his best figures for New Zealand were four for 25 and five for 61 against the MCC in 1906–7. He retired from cricket in 1910, but was elected a life member of the Carisbrook Cricket Club in 1911, served three terms as president, and was appointed life governor in 1960. He made a return to club cricket during the First World War and his non-selection for the Otago team in 1917–18 caused bitter argument.
Fisher was also a successful golfer. In 1903 he won the Otago Golf Club championship having in the same year set a course record of 79 on their Balmacewen links. On the same course in 1904 he won the New Zealand championships. After 1918 he began to own and race horses, with some success in major races at Riccarton, Christchurch.
In his earlier years Fisher was a frequent contributor to exhibitions by local artists. He served a term as president of the Dunedin Public Art Gallery Society, and his association with the gallery lasted 50 years. In 1912 he assumed his father's position as general manager of the Standard Fire and Marine Insurance Company, having spent the previous 12 years as manager of the Dunedin branch. He remained in the position for 35 years. He was twice president of the Dunedin Club.
On 15 December 1896, at Dunedin, Arthur Fisher had married Janet Graeme Rollo Brodrick. Following her death on 23 September 1928, he married Elizabeth Charlotte Farrant at Dunedin on 16 December 1930; Elizabeth Fisher died on 15 December 1957 and Arthur died aged 90 at Dunedin on 23 March 1961. There were no children of either marriage. He had retained all his faculties and remained remarkably active. Interviewed on his 90th birthday, he gave this advice: 'Live life easily, don't drink too much, don't play games too strenuously, cultivate a sturdy constitution and don't abuse it.' His portrait in oils, painted by Girolamo Nerli, was hung in the Carisbrook Cricket Club.