Šestić began his professional career at the JNA Symphony Orchestra in Belgrade, Serbia. He was a musician at the Military Orchestra in Split, Croatia, where he lived from 1984 to 1991.
Šestić kicked off his professional life at the JNA Symphony Orchestra in Belgrade, Serbia. He then moved on to become a musician with the Military Orchestra in Split, Croatia, where he lived and worked for about seven years from 1984 to 1991.