Trevor Llewellyn Woodgate was born on 4 September 1917 at Brisbane, Queensland to Frank Woodgate and Mary Rhoda Gwendoline Jones. He was one of five children; his siblings named Ronald Archibald Woodgate, Olwen Gwynneth Woodgate, Mervyn Rees Woodgate, and Malcolm Frank Woodgate.

Woodgate worked as a teacher at Keysland State School, Queenland before enlisting as a Flying Officer in the Royal Australian Air Force on 2 March 1941 in Brisbane, Queensland. He served with both the 1 Air Observer School at Evans Head, New South Wales and the General Reconnaissance School at Bairnsdale, Victoria, and was involved in bombing raids in Timor.

Woodgate married Sybil Gwendoline Boisen on 23 March 1943 at Wondai, Queensland and their son was born on 7 February 1944. Trevor Llewllyn Woodgate died in an aircraft accident near Ballina, New South Wales on 22 May 1944 at the age of 26. He was buried in Evans Head War Cemetery, New South Wales.