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.
He was at Vernon, in Normandy, in October 1789, when a furious mob fell upon a corn merchant, Planter by name, who had been charitable to the poor, but who, having sent flour to Paris, was accused of wishing to starve the town.
He was shortly afterwards summoned to Paris, January 1790, when he was presented by the assembly with a uniform sword of the national guard, and a civic crown was placed on his head.
[1][2][3][4] In June 1790 he was appointed to HMS Salisbury, bearing the flag of Vice-admiral Milbanke, who had, as his flag-captain, Edward Pellew, afterwards Viscount Exmouth.
On 29 April 1802 he was advanced to post rank, and from October 1804 to February 1805 was captain of HMS Foudroyant, in the Bay of Biscay, with the flag of his kinsman and connection, Rear-admiral Sir Thomas Graves.
On 15 April 1809 the Intrepid suffered severely in an unsuccessful attack on two French frigates under the guns of Fort Mathilde of Guadeloupe; and in December she returned to England and was paid off.