Zink joined the Junge Union in 1951 and joined the CDU in 1953. He was elected to the state executive committee and was deputy state chairman of the CDU Hessen from 1967 to 1992. From 1962 until his resignation on October 18, 1965, he was a member of the Hessian state parliament. He was a member of the German Bundestag from 1965 to 1990. He had initially entered parliament via the Hesse state list and represented the constituency of Groß-Gerau from 1983 to 1990. From 9 September 1981 to 1987 he was Deputy Chairman of the Bundestag Committee for Labour and Social Affairs.
Herbst, Ludolf; Jahn, Bruno (2002). Vierhaus, Rudolf (ed.). Biographisches Handbuch der Mitglieder des Deutschen Bundestages. 1949–2002 [Biographical Handbook of the Members of the German Bundestag. 1949–2002] (in German). München: De Gruyter - De Gruyter Saur. p. 1715. ISBN978-3-11-184511-1.
Speaker: Marieluise Beck-Oberdorf, Petra Kelly, Otto Schily until 3 April 1984; Annemarie Borgmann, Waltraud Schoppe, Antje Vollmer until 30./31. January 1985;
Sabine Bard, Hannegret Hönes, Christian Schmidt until 1 February 1986; Annemarie Borgmann, Hannegret Hönes, Ludger Volmer until 18 July 1986); Willi Hoss (8 September 1986)
Speaker: Thomas Ebermann, Bärbel Rust, Waltraud Schoppe until 26 January 1988; Helmut Lippelt, Regula Schmidt-Bott, Christa Vennegerts until 30 January 1989, Helmut Lippelt, Jutta Oesterle-Schwerin, Antje Vollmer until 15 January 1990; Willi Hoss, Waltraud Schoppe (until 21 June 1990), Marianne Birthler (from 4 October 1990), Antje Vollmer