He was director of his family's firm, John Graham (Dromore) Ltd., engineering contractors (est. c. 1788) from 1955. Graham Construction remains one of the largest construction firms in Northern Ireland and operates throughout the UK.
Graham was Chairman of the Standing Committee of the Ulster Unionist Council from 1947 to 1963. He was Chairman of Dromore Urban Council (1928–32) and of Iveagh Unionist Association (1935–65), and President of the latter from 1965 until his death.
Having been knighted in 1952 he was, in 1964, created Baronet, of Dromore, County Down. There were nine baronetcies created in 1964, no more were created until 1990, when Denis Thatcher was a recipient. Sir Clarence was succeeded by his son, John Moodie Graham (born 1938), upon his death. Sir John Graham, the second baronet, lived in Fort Lauderdale, Florida before returning to Northern Ireland
|Baronetage of the United Kingdom|
John Moodie Graham