He was born in Malin, County Donegal, Ireland and studied theology at Belfast College, the University of Glasgow, the University of Edinburgh and New College, Edinburgh.
In 1869, that newspaper merged with the Morning Telegraph to form the St. John Daily Telegraph and Morning Journal (later the Telegraph-Journal), with John Livingston as owner and Elder as editor.
In 1872, Elder ran unsuccessfully for a seat in the House of Commons of Canada.
He was elected to the Legislative Assembly of New Brunswick in an 1875 by-election held after the death of Joseph Coram.
In 1883, he was named provincial secretary, president and chairman of the Board of Agriculture.