William Alabaster was born in London, United Kingdom during 1890. He was educated at a state school in East Ham, London and immigrated to Australia in 1911. At the outbreak of the First World War he was working in the building trade as a carpenter and joiner.

Alabaster enlisted in the Australian Imperial Force on 27 October 1914 and was assigned to the 13th Infantry Battalion. He departed Sydney aboard HMAT Ulysses on 22 December 1914. After completing training in Egypt he was deployed to Gallipoli on 12 April 1915. He was wounded on 20 May 1915 and did not re-join his unit until 30 October 1915. Following the evacuation of Gallipoli, Alabaster was transferred to the 45th Battalion and arrived in France on 8 June 1916.

Alabaster was awarded the Military Medal on 23 June 1917 for organising and repeatedly leading parties of men over open country during intense bombardment to supply the front lines with munitions. He received several promotions and was promoted to Pioneer Sergeant on 14 April 1916.

William Alabaster died of wounds received from a shell at Doullens on 5 April 1918. He is buried at Doullens Communal Cemetery in France.