Conway articled until he was called to the bar in 1989 and practiced at Soloway Wright LLP from 1987 to 1994.
[3] In June 2021, Conway was retained to represent Maj Gen Dany Fortin in a judicial review application to the Federal Court of Canada, challenging the decision of government Ministers to remove him role as the head of Canada's procurement and distribution of COVID-19 vaccines.
Conway was recognized in 2007 by the National Post as one of Canada's top corporate and commercial litigation lawyers.
He has been recognized annually by Lexpert and Best Lawyers in Canada as a leading practitioner in corporate, commercial and products liability law.
[5] From 2004 to 2009, Conway was an adjunct professor of law the University of Ottawa, where he taught trial advocacy.