After joining the youth system of Red Star Belgrade, Šestić made his senior debut in late April 1974 (away against Olimpija Ljubljana and at home versus Čelik Zenica).

After helping them win the Yugoslav Second League in 1987, Šestić eventually won the national championship with Vojvodina in the 1988–89 season.

[2] At international level, Šestić was a member of the Yugoslavia national team at one European Championship (1984) and one World Cup (1982).

Šestić was critical of his team's role at the UEFA Euro 1984, commenting: We were very happy when Radanović scored in Split but maybe it would have been better had we not even went to France.

The only thing that should be remembered (from that tournament) is the excellent role of young Stojković who showed his huge amount of potential.