Around 1780 Henry Paulet (age 12) joined the navy as a midshipman. He spent 11 years at this rank.

In Feb 1789 Henry Paulet (age 21) was made junior lieutenant aboard HMS Crown at Spithead, Solent. HMS Crown became the flagship of Commodore William Cornwallis (age 45), who sailed with a squadron to India. Paulet reached Tenerife with the ship, but on the squadron's arrival there he was transferred to the frigate HMS Phoenix in exchange for one of the Phoenix's lieutenants. Paulet completed the voyage to India with the Phoenix, but shortly after his arrival he learnt that he was not to be taken back aboard the Crown. He was invalided back to Britain aboard the East Indiaman Houghton.

In 1791 Henry Paulet (age 23) was appointed to HMS Vulcan as a lieutenant.

In Apr 1792 Henry Paulet (age 25) was moved to HMS Assistance.

On 20 Feb 1793 Henry Paulet (age 25) was promoted to master and commander, and command of the sloop HMS Nautilus. He commanded the Nautilus as part of John Laforey's naval force that captured Tobago on 15 April 1793.

On 09 Jan 1794 Henry Paulet (age 26) was promoted to post-captain and was given command of HMS Vengeance by Sir John Jervis (age 59). Paulet served as flag captain to Commodore Charles Thompson at the capture of Martinique.

Before 10 Apr 1795 Henry Paulet (age 28) was given command of the 32-gun fifth rate HMS Astraea, cruising in the English Channel under the orders of Sir John Colpoys.

On 10 Apr 1795 Henry Paulet (age 28) was awarded the Naval Gold Medal for his action against the 42 gun French Gloire, with 275 men aboard who suffered 40 killed and wounded, while Astraea, of 32 guns and 212 men, had only eight wounded.

After 10 Apr 1795 Henry Paulet (age 28) was given command of the 36-gun frigate HMS Thalia, attached to Lord Bridport's fleet. He was present at the Battle of Groix, afterwards taking on board the fleet's flag captain, William Domett, and one of the captured French captains.

On 12 Jun 1798 Henry Paulet (age 31) was brought to court-martial aboard HMS Prince for having struck one of the Thalia's lieutenants, Robert Forbes. The offence being proved, the court had no choice but to dismiss him from the service. In view of the mitigating circumstances, the court recommended that Paulet be considered for clemency by King George III (age 60). The King was pleased to follow the recommendation and reinstated Paulet in the service.

After 12 Jun 1798 Henry Paulet (age 31) was given command of the 74-gun HMS Defence. He went with Sir Hyde Parker to the Baltic in 1801 and while he and the Defence were present at the Battle of Copenhagen, they were kept with Parker's reserve squadron and took no part in the fighting.

On 01 Aug 1811 Henry Paulet (age 44) was appointed Colonel of Royal Marines.

On 12 Aug 1812 Henry Paulet (age 45) was promoted to Rear-Admiral.

In 1813 Henry Paulet (age 45) was appointed one of the Lords Commissioners of the Admiralty which position he held until 1816.

On 02 Jan 1815 Henry Paulet (age 47) was appointed Knight Commander of the Order of the Bath.