Charles Stewart Dempster was born to a Scottish master mariner, Charles Dempster, and his wife, Eliza Jemima Weavers, in Wellington on 15 November 1903. He lived much of the first 30 years of his life close to Wellington's cricket ground, the Basin Reserve. Playing for the Wellington Boys' Institute team, he developed skills that drew him to the attention of the provincial selectors. He was encouraged by his father to score centuries for a reward of five shillings each, and he managed 9 centuries in 10 games in his most prolific season (his other game produced an innings of 99).
After representative appearances in primary and secondary school teams, 'Stewie' Dempster made his first-class début for Wellington in 1921–22, having averaged 50.80 runs as a 17-year-old in his first season of senior club cricket. Stocky and compact in build, Dempster was a right-handed opening batsman and an outstanding cover fieldsman. His New Zealand début, in 1924–25, was against the touring Victorian state team. He was selected to tour Australia in 1925–26, but was forced to withdraw. On New Zealand's first tour of England in 1927 the constant diet of cricket allowed him to blossom: 'That tour not only taught me not to do certain things which I had been in the habit of doing, but, more important still, the experience of English bowlers on English wickets opened my eyes to the real possibilities of how to make runs.' The tour produced his maiden first-class century, 180 against Warwickshire. Dempster finished top of the averages with 1,430 runs at 44.68.
New Zealand was awarded test status for the 1929–30 series against the MCC. Dempster scored the country's first test century in the second test at Wellington during an opening stand of 276 runs with Jack Mills. Their stand remains New Zealand's test opening record against England.
Dempster's return to England in 1931 was an even greater triumph. His 212 against Essex remained his highest score, and his form drew comparisons with that of Don Bradman the previous year. Dempster played in only the first test, scoring 120 in the second innings. New Zealand's performance in this game, and in previously beating an MCC eleven by an innings, saw two further tests added. Injury kept Dempster out of the second test, while the third test was rained out. He topped the aggregate for the tour with 1,778 runs, and the averages, at 59.26. He was selected as one of the Wisden Cricketers' Almanac's five players of the year.
Stewie Dempster played what he considered his most rewarding innings, against England, at Eden Park in 1933. Arriving late at the ground because the overnight express from Wellington was held up, he had to go in and face a hat trick. His 83 not out was outstanding in New Zealand's total of 158. The night that test finished Dempster sailed for England, where he worked for a cricket benefactor, Sir Julien Cahn. He duly qualified, as an amateur, to play for Leicestershire, a side he captained from 1936 to 1938. In 108 innings for the county he scored 4,659 runs. On 27 October 1938 Dempster married Margaret Elizabeth Jowers at Leicester Holy Trinity Church.
Dempster visited New Zealand with Cahn's team in 1939. Following his return to England, he held commissions in the Royal Armoured Corps and Pioneer Corps before being invalided out of the army. After divorcing his first wife he married Elsie Lowick in Birmingham on 12 September 1945; they had one daughter. The family moved to New Zealand in 1946. Dempster was to have played again for New Zealand in 1946–47 against England, but in a golfing accident a sliver of gorse pierced his left eye and he was forced to withdraw.
In New Zealand Dempster worked for a textile business, which involved travel between Wellington and Auckland. He and his wife divorced in 1958. On 27 December 1968, at Wellington, he married Tresna Havergal Aitken (née Voice), the widow of his lifelong friend, Bill Aitken, and the godmother of his daughter. Dempster died in Wellington on 14 February 1974, survived by his daughter and third wife.
Stewie Dempster's record of 12,145 first-class runs at 44.98 and 723 test runs at 65.73 places him among the best of New Zealand's batsmen. Between 1927 and 1933 he four times won the Redpath Cup for batting. In his later years he coached many young cricketers who went on to play for New Zealand. He is commemorated in the C. S. Dempster gates at the Basin Reserve.