He studied at the Séminaire de Nicolet, then studied law with Charles Dewey Day in Montreal and was called to the bar in 1836. He set up practice in Montreal and defended a number of persons involved in the Lower Canada Rebellion. Drummond, a supporter of Louis-Hippolyte Lafontaine, was elected  to the Legislative Assembly for the city of Montreal in an 1844 by-election, but was defeated in the general election that followed.
He attended the Séminaire de Nicolet, then studied law under Charles Dewey Day in Montreal and was admitted to the bar in 1836. He established a legal practice in Montreal and defended several individuals involved in the Lower Canada Rebellion. Drummond, an advocate for Louis-Hippolyte Lafontaine, was elected to the Legislative Assembly for the city of Montreal in a by-election of 1844, but lost the general election that followed.