Holburne had known Lord Morton as an intimate family friend and may well have owed his advancement in the Navy to Archibald Campbell, 3rd Duke of Argyll who "took him by the hand in his younger days and made him a captain". Promoted to post-captain on 15 February 1740, he was given command of the sixth-rate HMS "Dolphin". He transferred to the fourth-rate HMS "Argyll" in 1743 and to the fourth-rate HMS "Pembroke" in 1746 and then became commodore and commander-in-chief at the Leeward Islands with his broad pennant in the third-rate HMS "Kent" in 1748 during the War of the Austrian Succession. He went on to take command of the fourth-rate HMS "Tavistock" in 1749 and the second-rate HMS "Ramillies" in 1755.