Harry H. Elliott, second son of Sir Charles B. Elliott*, studied at the South African College in Cape Town from 1881, passing the matriculation examination of the University of the Cape of Good Hope in 1884. Continuing his studies at the college he passed the university's examination for the Certificate of Proficiency in the Theory of Land Surveying in 1886, and the next year was admitted as a land surveyor in the Cape of Good Hope. During 1888 he surveyed five pieces of Crown land in the Malmesbury and Cape divisions. He joined the Cape civil service in October that year and in due course became assistant engineer in the Eastern System of the Cape Government Railways, stationed in East London, though in 1896 he was in an acting capacity in Kimberley. Subsequently he was appointed acting district engineer at East London (September 1896), district engineer at Mafikeng (March 1897), acting resident engineer for the Queenstown to Tarkastad railway (June 1899), resident engineer for the Kalabas Kraal to Hopefield railway (July 1901), and resident engineer for the Western System, stationed in Cape Town (July 1904). In September 1910, following the formation of the Union of South Africa, he was appointed as maintenance engineer in the South African Railways and Harbours, stationed at its headquarters in Johannesburg. He held this post until his death at the age of 45 in 1914.
Elliott was an associate member (from February 1894) and later a full member (from January 1911) of the (British) Institution of Civil Engineers. He joined the Cape Society of Civil Engineers (founded 1902) soon after its formation. In October 1906 he read a paper, "Notes on railway construction and working in South Africa" which was published in the society's Minutes of Proceedings (Vol. 4). In 1907 he was a member of the society's council, serving as joint vice-president in 1909 and as president in 1910. His membership continued when the society became the South African Society of Civil Engineers in 1911. He served as joint vice-president again in 1913.