Born in Zaječar,[2] Kostić passed throw through the Radnički Niš youth categories[3] and later started his senior career with Timočanin in the 2013–14 season,[4] making 7 appearances in the Serbian League East.[2] He also continued playing with the club as a bonus player in the next season. In the winter break-off season, he was elected for the best sportsman of Knjaževac in 2014.[5] Playing for Timočanin, Kostić made 40 appearances in the Serbian League East at total between 2013 and 2015.[2]
^"Kostić iz Pirota u Metalac". fudbal.info (in Serbian). 15 January 2017. Archived from the original on 15 January 2017. Retrieved 5 February 2017.{{cite web}}: CS1 maint: unfit URL (link)