Monckton's sister, Valerie Goulding, founded the Irish Central Remedial Clinic and became a member of the Seanad Éireann.

His father was a British lawyer and politician, and became chief legal advisor to King Edward VIII during the Abdication Crisis in 1936.

After Cambridge, Monckton immediately joined the Army, being commissioned into the 5th Royal Inniskilling Dragoon Guards, which was part of the British Expeditionary Force in France.

He then attended the Command and General Staff School in the United States, before joining the 3rd (King's Own) Hussars in Palestine in 1944, moving with it to Italy in 1944.

He then commanded the 12th Royal Lancers in Germany for two years, and next was promoted brigadier in 1961 and took a staff posting to the War Office as deputy director of personnel administration.

[citation needed] He was promoted major general in 1963, and became Army director of public relations, dealing with press scrutiny into the behaviour of soldiers in Germany in the aftermath of unhelpful comments from the Secretary of State for War, John Profumo.

He regularly attended the House of Lords, having succeeded to the Viscountcy in 1965, speaking on rural affairs and the armed forces.