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He was educated at Eton. In 1796, he became Lieutenant, then Captain in the British Army, and he served in West Indies and Egypt. In 1803, as a brevet major, he announced the capture of St. Lucia. In defense of Sir Thomas Picton in 1804, he was jailed for three months for libel. However, a few years later he was again in the limelight as ADC to the prince Regent. He retired from the army as colonel
Back in Mauritius, he served in different capacities, namely as Chief of Police, Colonial Secretary, Collector of Customs, Civil engineer, Registrar of Slaves, Magistrate and Colonial Treasurer. In 1818, he was suspended by General Cage Hall but once more his powerful friends in England came to his rescue and Draper was reinstated. In 1822 he married a Mauritian lady named Lucie de Krivelt. Draper supported the Mauritian planters against the British official in respect of slaves trade and the abolition of slavery issues.
Dismissed by Governor Nicolay in 1832, he was sent back to England. In 1836, he was back again in Mauritius, this time he was appointed Colonial Treasurer and Paymaster General. Draper died on 22 April 1841 and was buried at Riviere Noire.