Peek joined the Royal Australian Navy College in 1928 as a cadet midshipman and graduated with maximum honours.

[2] He was consolidating his training as a gunnery officer, serving in the battleship HMS Revenge, at the outbreak of the Second World War.

[4] Peek was additionally decorated with the Distinguished Service Cross for "Gallantry and skill" during assault operations on the Lingayan Gulf.

During the Korean War, he commanded the destroyer HMAS Tobruk and for his service was awarded the United States' Legion of Merit.

From 1965 to 1967, he was Deputy Chief of Naval Staff, and from 1967 was Flag Officer Commanding HM Australian Fleet, which included oversight of the British Commonwealth's Far East Strategic Reserve.

During this period the RAN first participated in naval bombardment operations against North Vietnam, beginning with HMAS Hobart.