Arthur Donald Stuart Duncan was born at Colombo, Ceylon (Sri Lanka), probably on 6 August 1875, the son of John Duncan, a merchant, and his wife, Emily Georgina Macartney. Duncan arrived in New Zealand in January 1881 with his parents, two brothers and two sisters. The family lived in Te Puke until September 1882 when John Duncan became manager of the Wellington mercantile firm Levin and Company; in April 1889 he was made a partner in the business. Arthur Duncan attended Wanganui Collegiate School from 1888 to 1893 and while there excelled in many sports. He won the senior swimming and athletic championships, was captain of the First XI cricket team and a member of the rugby First XV. In 1894, his first year after leaving school, he represented Wellington at rugby and cricket.
It was in golf, however, that Duncan achieved his finest successes. He won the New Zealand amateur championship 10 times between 1899 and 1926 and the New Zealand open championship in 1907, 1910 and 1911. He was the club champion at the Wellington Golf Club on 23 occasions, the Miramar Golf Club champion six times and the Hutt Golf Club champion four times. In 1927 he was a member of the first New Zealand team to play in international matches and was selected again in 1930 and 1935. In 1935, in his 60th year, he was third in the open championship and the leading amateur.
Duncan has been described as 'the compleat golfer, a wonderful stylist with particular mastery of his irons'. He had a superbly rhythmical swing and a devoted attention to the game, qualities that enabled him to play to a scratch handicap well into his 60s. He was an example to other golfers, not only as a player but also for his sportsmanship and for his courtesy on and off the golf course. 'He was modest in victory and never complained in defeat,' and was always willing to help other players, particularly younger golfers, who respectfully called him Mr Arthur. Duncan was well known for his immaculate dress on the golf course. After the Second World War he was frequently seen at the Wellington Golf Club in a cream silk shirt, gold cufflinks and a grey tie. He was captain of the club in 1931, 1932 and 1942 and president in 1941 and 1950. He served on the New Zealand Golf Association's council in the 1920s, and was elected president in 1950.
Duncan also had a successful business career. On leaving school he went to work with Levin and Company. After serving as cashier of the firm he became branch auditor. In 1923 he was appointed secretary to the company and from 1935 to 1938 was manager of the Masterton branch. He was elected to the board of directors in 1935 and on his retirement in March 1950 became chairman of directors. Duncan was married in Wellington on 29 January 1902 to Alice Marguerite Featherston Johnston, the daughter of C. J. Johnston, a prominent citizen and merchant.
Arthur Duncan died at his home in Murphy Street, Wellington, on 10 March 1951. He was survived by Alice Duncan and two daughters. No individual golfer had dominated New Zealand amateur golf for as long a period as Duncan. Speaking at the time of his death, Harold Black, the 1930 New Zealand amateur champion, said, 'His playing record was unique and his wonderful ability, his sportsmanship and his comradeship were at all times evident on the links – and these will ever remain a happy memory'.