Delme was born in Glanaman and spent most of his childhood in Llanedi near Ammanford.

He was educated at Amman Valley Grammar School and Cardiff University where he received a first class honours degree in zoology.

Delme was Executive Member for Traffic and Transportation, Cardiff County Council for the past three years and is a former Deputy Lord Mayor. He has wide experience in Local Government, having served as a Plaid Cymru member at Community, Borough, and County levels over the past 25 years.

He has represented Creigiau at County level for twenty years. He was for many years a member of Taff Ely Borough Council, Mid Glamorgan County Council and the WLGA.

He currently represents Creigiau and St Fagans on Cardiff County and is former Chair of Pontyclun and Pentyrch Community Councils.