Carrick Hey Robertson was born in Govan, Glasgow, Scotland, on 27 August 1879, the son of Robertson Blair Robertson, an oil merchant, and his wife, Jessie Cameron Gow. The family moved to London where Carrick was educated at St Dunstan's College. After a distinguished student career at Guy's Hospital, he graduated in medicine from the University of London in 1902. Two years later he gained his FRCS. He practised in Pietermaritzburg, Natal, for a year before taking up the position of honorary surgeon at Waihi Hospital, New Zealand, in early 1906. That year on 20 June, in Auckland, Robertson married Emmeline Constance Maxwell Hibberd, the daughter of the postmaster general of Natal.
From 1907 to 1912 Robertson was medical superintendent at Waihi Hospital. He then moved to Auckland where he set up in private practice and was appointed an honorary surgeon to Auckland Hospital. He was also associated with the Mater Misericordiae Hospital (now the Mercy Hospital), first as senior surgeon and later as chief of staff. In the First World War he served as a temporary major with the New Zealand Medical Corps on the hospital ship Marama in 1915–16. He returned home early because his wife, who was due to have a baby, was ill.
An outstanding operator of near flawless surgical technique, Robertson remained a general surgeon throughout his career. He gained a worldwide reputation for surgery for goitre, which was then a common complaint in New Zealand, and was a local pioneer of brain surgery. In 1927 he performed, with the help of Dr Casement Aickin, what was probably the first heart operation in New Zealand in an attempt to save the life of a patient, who had developed severe complications following an acute ear infection. The patient survived the operation but succumbed within days.
Many honours came Robertson's way. In 1924 he was president of the New Zealand Branch of the British Medical Association and the same year was made an honorary fellow of the American College of Surgeons. He was a founding fellow of the College of Surgeons of Australasia (later the Royal Australasian College of Surgeons), and in 1947 became an honorary fellow of the Association of Surgeons of Great Britain and Ireland. Knighted in 1929, he was dubbed at an investiture in St James's Palace, London. In 1938 he was made a chevalier de la Légion d'honneur.
Robertson played a key role in establishing the school of nursing at the Mater Hospital in 1937. He lectured regularly to the student nurses and his lecturing often carried beyond the classroom: when he was operating and felt there was something his pupils should see, he would say, 'Send for the girls.' Although he retired from the post of honorary surgeon to Auckland Hospital in 1937 and was appointed a consulting surgeon, he continued for some years to operate at the Mater Hospital.
Outside medicine, Robertson was president of the Northern Club, Auckland, and convener of its wine committee for many years. He was also president in 1936–37 of the Auckland Institute and Museum and a member of its council for nearly 40 years. He went on scientific expeditions to islands in the Hauraki Gulf and in 1956 donated £600 to be used for research on Auckland's offshore islands. His wife, Constance, died in 1950 and on 16 May 1957, in Sydney, he married Delta Clark, née Cranwell. Carrick Robertson died at the Mater Hospital, Auckland, on 14 July 1963, survived by his second wife and four children of his first marriage.
Robertson possessed a kind and friendly character. He was regarded as a 'delightful host', was keen on golf, tennis and billiards and was a skilled trout fisherman. In his chosen field of surgery he was brilliant and innovative, advancing the techniques of standard operations, such as thyroid surgery, and was always ready to develop new procedures, as in brain and heart surgery. He was a superb surgical teacher and, as a consultant, his opinion was widely sought.