He was born in 1947 in Victoria, British Columbia to Commodore F. Dudley Elcock and Mary Grace Pitfield and is the oldest of four children (Hew, Julia and Mark (deceased)).

He is the nephew of former Clerk of the Privy Council of Canada, the retired Senator late Michael Pitfield, and retired financier Ward C. Pitfield, Jr. A Bachelor's graduate in Political Science from Carleton University, Elcock received his LL.B.

Elcock served as the Security & Intelligence Deputy Clerk of the Privy Council Office for five years, and as Assistant Secretary to the Cabinet (Legislation and House Planning/Counsel) for six years, prior to his rise to CSIS and National Defence.

In 2007, Elcock was named Senior Advisor to the Privy Council Office "pending his next assignment".

Between 2010 and 2016 he was Special Advisor on Human Smuggling and Illegal Migration in the Privy Council Office.