He was educated in Sackville, studied law with Edward Barron Chandler and was admitted to the bar in 1846.
Palmer practiced law in Dorchester until 1867 when he moved to Saint John.
Palmer was elected to the House of Commons of Canada as a member of the Liberal Party of Canada on October 12, 1872, to represent the riding of the City and County of St. John, New Brunswick and he was re-elected in 1874, but was defeated on September 17, 1878.
Palmer also served as president for the New Brunswick bar association.
His brothers Rufus and Martin served in the New Brunswick assembly.