Born in Kütahya in 1962. He graduated from Gazi University Public Administration in 1985. Between 1988-1990, Zeybek served as an inspector in Gima T.A.Ş. and between 1990-1994 he served in the Vakıfbank Inspection Board. Between 1994-1995 he served as Vakıfbank Deposits Directorate and between 1995-1996 as the Director. During 2002-2008 Zeybek served as Vakıfbank Ankara Branch Manager and between 2014-2015 he served as Executive Vice President in Göknur Gıda A.Ş. He is the co-founder and Chairman of As Finansal Danışmanlık established in 2015 to provide financial consultancy to firms.