Born into an aristocratic family in London, Leese began his military experience in 1909 by enlisting in the Officers' Training Corps whilst he was a student at Eton 

When the First World War broke out, he volunteered to join the British Army as Second Lieutenant in the Coldstream Guards, and from October 1914 was deployed to the French front. In this role, he fought and was wounded several times, including during the Battle of the Somme where he received a medal of merit.

After the war, Leese decided to remain in the British Army, continuing his studies and climbing the military hierarchy until he became a colonel in 1938. That year, he obtained a position as a trainer in India. Eager to take part in the European fighting of the Second World War, in March 1940 Leese requested and obtained a transfer to England. Shortly thereafter, he was employed in France following the British Expeditionary Corps. There he worked on the organisation of the evacuation of British forces from the beaches of Dunkirk, also returning to England along with the troops.

In September 1942, after a long series of promotions, Leese was sent to Egypt in command of XXX Corps, as part of the campaign orchestrated by General Montgomery. The Corps led by Leese, after being engaged at El Alamein and reaching Tunis, was employed in Operation Torch and eventually sent back to England to begin preparations for the invasion of Normandy.

However, in December 1943 Leese was recalled to Italy to take Montgomery's place in command of the British Eighth Army, which was meanwhile involved in fighting along the Gustav Line. He then led his troops in the Battle of Monte Cassino in May 1944 before receiving a new assignment that led him to leave the Mediterranean theatre. From September 1944, he assumed command of the 11th Allied Army Group in Asia, active in the Burma (now Myanmar) campaign.

After his wartime experience, which had ended in disagreements with the Supreme Commander of Southeast Asia, Louis Mountbatten, Leese was relieved of his command and recalled to England, where he decided to retire from the army in 1947. He died in Wales in 1978 at the age of 83.