West was commissioned lieutenant on 11 April 1769 and promoted commander on 30 May 1777, being appointed to the sloop Zephyr 14. On 23 August 1778 this vessel was captured by the French corvette Gracieuse 26 and carried into Toulon. After being exchanged he commanded the Alderney 10 from June 1780.
On 19 October 1780 he was posted captain, joining the Champion 24 which sailed in March for the African coast where he saw action against a Dutch settlement on the Gold Coast. He then went on to the Leeward Islands, being present at the Battle of St. Kitts on 25/26 January 1782, following which he moved into the Shrewsbury 74, a vessel that was so battle weary that she was shortly condemned as unfit for service, thereby causing him to miss the Battle of the Saintes on 12 April. Immediately following that engagement he joined the Repulse 64 in which he sailed to North America with the fleet under Admiral Hugh Pigot in the autumn, returning to the Leeward Islands before sailing with the fleet for Jamaica in April 1783 and being paid off in July.
In March 1789 West commissioned the Medway guardship Director 64, being present at the King’s Naval Review at Plymouth on 18 August, and retaining her during the Spanish Armament of 1790. He then had the Alfred 74 in the Russian Armament of 1791, and commanded her in the Medway as a guardship until the following year.
His final command, from August 1793 until April 1794, was the Alexander 74.
West was advanced to flag rank on 14 February 1799, became a vice-admiral on 9 November 1805, and an admiral on 31 July 1810.