Before taking office, he worked as an Assistant Professor and Vice-Dean for International Cooperation at the Faculty of Political Science in Podgorica.

In 2008, Vuković defended his masters thesis on the topic of "European Integration and Political Competition in Montenegro: The Determinants of Party Consensus".

Vuković spent academic year 2016–2017 at George Washington University as the first Fulbright Postdoctoral scholarship holder from Montenegro.

In 2018, Vuković publicly supported the presidential candidate of the Democratic Party of Socialists (DPS), Milo Đukanović.

Vuković stated: Today, I come to you as a free man, proud and humble, ready to put absolutely everything I have learned in my life for the purpose of the future development of our City, convinced that there are no shortcuts to success and that what each of us wishes upon our City of Podgorica can only come as a result of a hard work.