Career
Galešić started his career in the youth squads of Borac Banja Luka. In 2007 he joined the Slovenian side Gorica, where he stayed until the summer of 2010, when his contract with the club expired. In June 2010 it was reported by the media that Galešić has signed a three-year contract with the Serbian team Partizan.
However, in September 2010 Galešić returned to Gorica after negotiations failed with Partizan.
Galešić signed a two-year contract with possible extension for another year. In 2012, he signed a one-year contract at Beerschot Air Corps and played in several matches, before being released in December of the same year.
In June 2013 he signed a contract with Hajduk Split but 3 weeks later in July 2013, his contract was mutually terminated after continuous racial abuse from a small, radical minority of Hajduk"s fans. Botev Plovdiv
Galešić signed a two-year contract with Botev Plovdiv on 22 August 2014.
He made an unofficial debut for his new team during the friendly game with Rakovski.
Galešić made a debut for Botev Plovdiv in A Grupa on 12 September 2014. He was brought on as a substitute during the second half in the match against Ludogorets Razgrad. He played well and was involved in the goal scored by his team but it was not enough because his team had conceived two goals before his appearance on the field and Botev Plovdiv lost the game 1–2.
At the end of 2014 Goran Galešić became a free agent after a mutual termination of his contract with Botev Plovdiv.
Galešić was a part of the Bosnia and Herzegovina national under-21 football team