He was Romania’s Ambassador to the State of Kuwait and the Sultanate of Oman (1991-95), Egypt (1997-2001), UN and other international organizations in Geneva (2003-09) and to China and Mongolia (2012-17). While in Geneva, Costea was the first representative of an EU Member State to be elected President of the UN Human Rights Council (2007-08) and steered the setting up of HRC new mechanisms (the Universal Periodic Review, the Review of Mandates of Special Procedures and others).
He lectured, inter alia, at the American University of Cairo, the Harriman Institute for Russian, Eurasian and Eastern European Studies at Columbia University (New York), Tsinghua University, the Institute for International Studies, the Chongyang Institute for Financial Studies with Renmin University China Academy of Social Sciences in Beijing and at the Sun Yat-sen University, Guangzhou (Canton). Costea is a guest lecturer of the Romanian Diplomatic Institute and was a panelist and moderator at several editions of the Bucharest Forum organized by the Aspen Institute Romania and the German Marshall Fund; likewise, he was speaker at meetings of the China Strategy Group with European Center on Foreign Relations. He is fluent in Arabic, English and French and has a Ph.D. in political science (2009) with the National School of Political and Administrative Studies, Bucharest, on democracy building in the Middle East.