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. He then served in the Naval Brigade during the Indian Mutiny and was present at the Capture of Lucknow. He was promoted to Lieutenant in 1861. In 1863, he was appointed to serve on HMS "Revenge". On 10 November 1864, his brother Lord Albert was court-martialled on board HMS "Victory" at Portsmouth. Charges of "desertion and breaking his parole" were upheld by the court and Lord Albert Pelham-Clinton was sentenced to be dismissed from the navy, although "The Times" reported that the case referred to Lord Arthur in error.