In 1917, Zaunius defended his doctoral thesis in criminal and civil law at the University of Königsberg.

Zaunius began his diplomatic career after his appointment as Envoy Extraordinary and Minister Plenipotentiary of Lithuania to Czechoslovakia and Romania (1924–1925).

In 1927, after the liquidation of the Lithuanian representation at the League of Nations, he returned to Lithuania and was appointed as secretary-general of the Foreign Ministry and envoy to Czechoslovakia.

During his tenure, Lithuanian diplomats achieved some success at the Permanent Court of International Justice in cases against the Second Polish Republic (concerning rail traffic on the Libau–Romny Railway) and the Weimar Republic (concerning the dismissal of Otto Böttcher, President of the Directorate of the Klaipėda Region).

In 1934–1936, he worked at the State Council of Lithuania, assisting with various agreements with foreign countries.