He was a lumber merchant at Trois-Rivières and also acted as an agent there for Mathew Bell. In 1844, he married Catherine, Bell's daughter. Greive served in the local militia, becoming lieutenant in 1825, and later served in a volunteer company of loyalist militia organized by Mathew Bell during the Lower Canada Rebellion. In 1837, with Bell, he purchased parcels of land in Brompton and Durham townships. He was named treasurer for Trois-Rivières district in 1841. Greive was elected to the Legislative Assembly of the Province of Canada for Trois-Rivières in 1844. He served for a committee that was balloted on January 18th,1845. The committee was made for the county of Lanark.