Cor was the eldest son of Andrew Cor, a merchant in Edinburgh. Cor became a burgess of Edinburgh in November 1566 and served the burgh council as a Dean of Guild, and Bailie. He acquired a property in
Advocates Close in 1579 and his house, built or rebuilt around 1590, is a rare survival of an Edinburgh merchant's house of this date. A
painted renaissance ceiling was discovered in the house in 2010 and dated by dendrochronology to Cor's period of ownership. His sister Isabella Cor died of the
plague in 1585. In September 1596, with the physician
Gilbert Moncreiff and kirk minister
Robert Bruce he interviewed a woman from Nokwalter in Perth, Christian Stewart, who was accused of causing the death of Patrick Ruthven by witchcraft. She confessed she had obtained a cloth from Isobel Stewart to bewitch Patrick Ruthven, and repeated this confession to the king and
Sir George Home at
Linlithgow Palace. She was found guilty of witchcraft and burnt on Edinburgh's Castlehill. Cor bought produce from
John Gordon, 13th Earl of Sutherland and expected cash payment in silver when the Earl was unable to supply the contracted "victual" from his tenant farms in 1602. Clement Cor's son-in-law, the Laird of Ardrie, made arrangements with the Earl. ==Fife and the Lewis venture==