David Gibson Alexander was born at Ballytiglea, Ireland. Alexander migrated to Australia about 1890 and was living and working as a barman in Sydney at the beginning of the First World War. At this time, his mother Annie Sophia Alexander was still living in County Carlow, Ireland.

Alexander enlisted in the Australian Imperial Force on 21 December 1914. He was assigned to the 13th Infantry Battalion and departed Sydney aboard HMAT Seang Choon on 11 February 1915. He was fatally wounded by shrapnel during the August landings at Suvla Bay and died at sea aboard HS Rewa on 15 August 1915. David Alexander is commemorated on the Lone Pine Memorial, Gallipoli, Turkey.