[1] Born in Zagreb, Ćosić came through the youth ranks and started his professional career at NK Inter Zaprešić.
A former youth international, he made his first-team and Prva HNL debut on 23 July 2011 in a 2–0 away loss to GNK Dinamo Zagreb, coming in the 77th minute for Stjepan Babić.
[2] Nevertheless, he continued on playing for the U-19 team, featuring only sporadically, until the club's relegation to the Druga HNL in the summer of 2013 when he became a first-team regular.
Ćosić made his Hajduk debut in a 2–2 away draw against CSMS Iași in the second round of 2016–17 UEFA Europa League qualifying, playing the full 90 minutes.
[5] Ćosić signed with Slovenian PrvaLiga club NK Rudar Velenje on 23 January 2019 until June 2020.