Nesham entered the navy in January 1782 on board HMS "Juno", with Captain James Montagu, and in her was present at the action off Cuddalore on 20 June 1783. On his return to England in 1785, he was for some time aboard HMS "Edgar", guardship at Portsmouth, commanded by Captain Adam Duncan, afterwards Lord Duncan, and aboard the frigate HMS "Druid" until March 1788.