Kostić took part in regular military service with the Yugoslavian armed forces in 2002–03, has been active with Orthodox Christian organizations, and began operating his own business in 2008.

No formal explanation was given, although Dveri members said it was because of his decision to invite Russian deputy Natalia Poklonskaya from the disputed territory of Crimea to the Serbian assembly.

[15] In the same month that he was dismissed as chair, Kostić received a medal from the Russian ministry of internal affairs at Poklonskaya's recommendation for strengthening ties between Serbia and Russia.

In early 2020, Kostić joined Dveri leader Boško Obradović in an eleven-day hunger strike on the steps of the national assembly, accusing the Progressives and their allies of undermining Serbia's state institutions.

The opposition boycott ended in 2022, and Dveri contested the that year's parliamentary election in an alliance with Žika Gojković's branch of the Movement for the Restoration of the Kingdom of Serbia (POKS).

In a statement released on the day of his election, Dveri pledged to support Serbia's political and economic sovereignty, uphold the traditional family structure, and protect the country's environment from what it described as the combined threat of Vučić's government and the Rio Tinto corporation.

[29] In December 2024, against the backdrop of growing anti-corruption protests, Kostić called on Serbian citizens to put aside "all ideological and political differences" to remove Vučić from power and establish functioning state institutions.

He supported the students driving the protests, saying, "They showed us that they do not want to live in a system where corruption, crime, nepotism, arrogance, negative selection, subservience and immorality of every kind reign.