He underwent recruit training at the Marine Corps Recruit Depot Parris Island, then attended a nine-week Demolition Specialist Course at Schools Battalion, Marine Corps Base Camp Lejeune, where he was promoted to private first class.
He was the last Sergeant Major of the Marine Corps to have served in the Korean War. Cleary enlisted in the United States Marine Corps on 24 October 1951. Upon completion of the school, he was assigned as the Battalion Demolition Specialist, Company B, 7th Engineer Battalion at Marine Corps Base Camp Pendleton.
Promoted to corporal, he remained with the 7th Engineer Battalion until April 1953.
Cleary transferred overseas, where he joined the 1st Marine Division in of Korea, as a Squad Leader and Right Guide with Company I, 3rd Battalion. While in this assignment, he was promoted to sergeant.
Returning from overseas, he reported to the 1st Rifle Company at the Navy and Marine Corps Reserve Training Center, Springfield, Massachusetts. In early 1958, he returned to Camp Pendleton, for duty as a military policeman with the Military Police Company.
In May 1958, he was promoted to staff sergeant, and continued to serve in this assignment until April 1961, when he transferred to the Marine Corps Recruit Depot San Diego for duty as a drill instructor.
Upon completion of his tour as a drill instructor, Sergeant Major Cleary joined Headquarters and Service Company, 2nd Battalion 5th Marines for duty as a Section Leader, and later, Platoon Sergeant in the 81 mm Motor Platoon. In February 1965, he transferred to H&South Company, 3rd Battalion, 3rd Marine Division, as a Platoon Sergeant and Platoon Leader. This assignment was followed by his first tour in Vietnam as a Platoon Leader, Company G, 2nd Battalion 1st Marines, where he was promoted to gunnery sergeant.
In August 1966, he transferred to Company F, 2nd Battalion 27th Marines, 5th Marine Division, for duty as Company Gunnery Sergeant.
He returned to San Diego for a short tour as a drill instructor in August 1967, at which time he was selected for promotion to first sergeant. He was reassigned to the 27th Marine Regiment as the Company First Sergeant.
During March 1968, he returned to Vietnam, serving as the First Sergeant of Battery C, 1st LAAM Battalion, MACC-19, 1st Marine Aircraft Wing. Subsequently, he served as Company First Sergeant of Company G, 28th Marine Regiment.
Cleary then reported to H&South Company, 2nd Battalion 7th Marines as the Company First Sergeant, followed by his third tour in Vietnam as the Squadron Sergeant Major of HMM-165.
In September, he was reassigned to the 2nd LAAM Battalion. He reported to Headquarters Marine Corps in September 1974 for duty as the Battalion Sergeant Major of Marine Security Guard Battalion, followed by duty as Personnel Sergeant Major. His next assignment was as the 3rd Marine Division Sergeant Major in July 1979, then returned to Marine Security Guard Battalion.
On 1 January 1982, Sergeant Major Cleary was selected as the Sergeant Major of Marine Corps Development and Education Command in Quantico, Virginia.
He was selected as the 10th Sergeant Major of the Marine Corps on 25 May 1983, and assumed the post on 28 June 1983. He retired in 1987.