He had three brothers and a sister, Lady Susan Vane-Tempest; she became a mistress of future King Edward VII of the United Kingdom in 1864, when he was the 23 year-old Prince of Wales.

Clinton was educated at Woodcote School, Reading, and then Eton College; he entered the Royal Navy in 1854 at the age of 14 and served during the Crimean War in the Baltic Campaign of 1854.

In his book Fanny and Stella, biographer Neil McKenna cites circumstantial evidence suggesting that Lord Arthur lived on in exile.

[9][15][16][17] On 8 February 1882, twelve years after Clinton's death, Mary Jane Fearneaux and James Gething were arrested in Birmingham and charged with obtaining £2,000 from one man and £3,000 from another under false pretences.

[18] Fearneaux was found to have been living for some years as a man in Birmingham while claiming to be Lord Arthur Clinton, saying that the reported death was a fiction contrived by family and friends to avoid disgrace.

[19] At the subsequent trial of the pair, Gething was acquitted and Fearneaux changed her plea to guilty; she was sentenced to seven years in prison.