Born in Čajetina,[1] Glišović played with Zlatibor Čajetina and Jedinstvo Užice in his youth career.[1] He joined the first team of Jedinstvo in 2013–14 season, but also stayed with youth team until the end of season.[2] He noted his first senior caps during the 2014–15 season, making four Serbian First League appearances.[3] At the beginning of 2015–16 season, Glišović played cup matches against Zemun[4] and Čajetina,[5] and later, during the season, he played mostly matches as a defender. He also played all 15 matches in the Serbian League West, during the first half of 2016–17 season, scoring a goal in the second fixture match against Budućnost Krušik 2014.[6] In the winter break off-season, Glišović was related with returning to Zlatibor,[1] but he continued playing with Jedinstvo.
