Şuay ALPAY was born in Elazığ on 20 October 1960.
He graduated the Faculty of Law of the Istanbul University.
He worked as assistant specialist at the Union of Public Employers in 1986.
He started his judicial internship in 1986 and served as judge in the field of criminal and civil law until 1991.
He worked as self-employed lawyer after 1991.
He was a Member of Parliament for the Elazığ constituency during the 24th and 25th terms.
He served as founder and director of non-governmental organizations.
He served as Member of Central Decision and Executive Council (MKYK) of the Justice and Development Party, Deputy Head of Local Administrations of Ak Party, Member of Constitution Committee, Member of Justice Committee, Parliamentary Group Chairman of Ak Party, Deputy Head of Ak Party Head Office, as member and chairman of inter-parliamentary friendship groups.
He was appointed as Deputy Minister of National Defence on 29 December 2015.
ALPAY is married and has 3 children.