Prinsep was the son of Charles Robert Prinsep, standing counsel to the East India Co. government and his wife, Louisa Anne, nee White. Charles Prinsep invested in the Adelphi estate in Van Dieman's Land and the Belvedere estate in Western Australia. Prinsep's mother died in 1853 and with his father, a few years later, in an advanced stage of paralysis, Prinsep was cared for by his uncle and aunt. He completed his schooling at Cheltenham, England and was given art lessons by George Frederick Watts. Prinsep later studied law at Oxford and art in Germany. His aunt, Sara Prinsep conducted an artistic and literary salon with Alfred (Lord) Tennyson (q.v.) a participant. Prinsep's sister became the second wife of Tennyson.
After his grand tour of Europe and the death of his father in 1865, Prinsep visited the family Belvedere estate, arriving in Fremantle, Western Australia, on 20 May, 1866. In October he met his future wife Charlotte Josephine, daughter of J. G. Bussell, and married her on 26 February, 1868. Falling prices in India and the colony led to the sale of the Belvedere estate to creditors in 1874. Prinsep moved to Perth where he was a draftsman in the Lands and Survey office and by 1894 was under-secretary of the Department of Mines. In 1898 he became Chief Protector in the new sub-department of Native Affairs. He tried unsuccessfully to alleviate the ill-treatment and neglect of the indigenous people. He retired in 1907, living in England until 1912 and dying in Busselton, Western Australia a decade later.
Prinsep maintained a continuing interest in art and literature, leading an influential group engaged in sketching excursions, literary discussions and the theatre. He published several numbers of Opossum, a humorous journal, with Henry Gibbs, another artist. Prinsep's 1875 and 1876 drawings relating to the explorations of (Sir) John Forrest and Ernest Giles were included in published accounts of their expeditions and commissioned by the Lands Department..In 1889 Prinsep was a founding member of the Wilgie Sketching Club (later the West Australian Society of Artists). He was its president in 1904-1905 and exhibited oils and watercolours with it in 1901-1908. Prinsep visited Europe in 1908 and was for some years mayor of Busselton in his retirement. He continued to write poetry as late as World War I.
(Source: Adapted from A. C. Staples, 'Prinsep, Henry Charles (Harry) (1844 - 1922)', Australian Dictionary of Biography, Volume 11, MUP, (1988): 298-299; 'Prinsep, Henry Charles (1844-1922)', The Dictionary of Australian Artists ed. Joan Kerr (1992): 643-644).