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He was born in County Monaghan but grew up in Belfast and was educated at Methodist College Belfast and Trinity College, Dublin. He was called to the Northern Irish Bar in 1944 and took silk in 1958. He served as senior Crown Counsel in Tyrone, Fermanagh and Armagh from 1958 to 1968.
In 1964, he was elected to the House of Commons of Northern Ireland as Ulster Unionist member for Mid Down. He was appointed as Attorney General for Northern Ireland in 1968. He was appointed to the Privy Council of Northern Ireland in the 1969, entitling him to the style The Right Honourable.
In March 1972, the entire Government of Northern Ireland resigned, and the Parliament of Northern Ireland was prorogued. As a result, Mr Kelly ceased to be Attorney General. The office of Attorney General for Northern Ireland was transferred to the Attorney General for England and Wales and Kelly was the last person to serve as Stormont's Attorney General. In 1973, he was appointed as a judge of the High Court of Northern Ireland, and then as a Lord Justice of Appeal of Northern Ireland in 1984, when he was also knighted and appointed to the Privy Council of the United Kingdom.
- "Members of the Northern Ireland House of Commons". United Kingdom Election Results. Retrieved 29 July 2016.
- "Judge in 'supergrass' trial dies". BBC News. British Broadcasting Corporation. 5 December 2008. Retrieved 2008-12-05.
- Flackes, W.D. and Elliott, S. (1989) Northern Ireland: A Political Directory (3rd ed.) Belfast:Blackstaff Press Ltd
|Parliament of Northern Ireland|
| Member of Parliament for Mid Down
Edward Warburton Jones
| Attorney General for Northern Ireland
Sir Peter Rawlinson