As a junior officer, he was deployed with a squadron under Admiral Edward Vernon to the West Indies at the start of the War of Jenkins' Ear.

He led a naval attack against the fortifications on Sullivan's Island (later called Fort Moultrie after their commander), protecting Charleston, South Carolina.

However, after a long and hard-fought battle, Parker was forced to call off the attack, having sustained heavy casualties, including the loss of a ship.

[1] Promoted to commander on 17 March 1735, he was deployed with a squadron under Admiral Edward Vernon to the West Indies in 1739 at the start of the War of Jenkins' Ear.

[2] Promoted to captain on 6 May 1747, he became commanding officer of the sixth-rate HMS Margate later that month and was deployed protecting commercial shipping, first in the Channel and then in the Mediterranean.

[2] In June 1776, Parker led a naval attack against the fortifications on Sullivan's Island (later called Fort Moultrie after their commander), protecting Charleston, South Carolina.

[3] After a long and hard-fought battle, Parker was forced to call off the attack, having sustained heavy casualties, including the loss of the sixth-rate HMS Actaeon, grounded and abandoned.