From 1991 to 1998, Alexander worked for the Otto Suhr Institute of Political Science (OSI) and the Institute for East European Studies (OEI) at Freie Universität Berlin (FU Berlin). He has also conducted research at the United Nations (UN) Secretariat in New York City (1996) and as part of the International Staff at NATO Headquarters in Brussels (1996-97).
From 1997 to 2016, he worked for the Organization for Security and Co-operation in Europe (OSCE), the European Union Monitoring Mission (EUMM) and the European Union Special Representative (EUSR) in the former Yugoslavia, mostly in Bosnia and Herzegovina. There, in his capacity as chef de cabinet and special adviser in the Office of the High Representative (OHR) and as deputy director of the Mostar Implementation Unit (MIU) during the tenure of Lord Paddy Ashdown, he was involved in the implementation of the Dayton Peace Accords.