Edward Randolph Cleaver was born at Ferntree Gully in Victoria in 1886. He attended Sale State School and later trained as a butcher. He enlisted at 29 with the Australian Imperial Force on 19 August 1914. According to his sister Adeline, Cleaver was the first man in the town of Sale to have enlisted. He departed Melbourne with the 4th Light Horse Regiment aboard HMAT Wiltshire on 19 October 1914.

Cleaver was deployed to Gallipoli in July 1915 and served there until the evacuation in December. He spent 1916 patrolling with his squadron around the Suez Canal in Egypt. Like many of the troops he wrote home regularly, sending photos of himself and his mates in their small canvas shelters in the desert. "The desert", he wrote, "was better than Gallipoli where they were being fired at day and night. In the desert we can get on our horses and ride into the distance to get away from the noise of war."

On 31 October 1917 Cleaver took part in one of the most famous actions of the First World War: the charge of the Light Horse at Beersheba. He was part of the first squadron to reach the enemy lines; his horse leapt over the first two trenches and then, as he dismounted to fight the Turks in the third trench, he was cut down by machine-gun fire.

Edward Cleaver is buried at the Beersheba War Cemetery, Palestine. Sadly, his father died just nine days later.