Between 1985 and 1989 he represented Altay SK, where he recorded 136 matches and 29 goals, and finished his career at Trabzonspor in 1989-90 with 37 matches and 9 goals in total.
He is immensely disliked amongst the Fenerbahçe supporters because they view him as responsible for an injury suffered by "Şeytan" Rıdvan Dilmen(Rıdvan the Devil) in 1990 during a league match between Fenerbahçe and Trabzonspor. Rıdvan never fully recovered despite undergoing sixteen operations, and eventually had to retire in 1995 at Fenerbahçe after painful years of injuries. Ješić had also accumulated a record number of bookings in his tenure in Turkish Süper Lig. Opponents claimed that he also injured many players in Turkey and gave him the nickname of "Kasap Jesic", which means "Jesic the Butcher"
As a manager, Ješić began his career at FK Obilić in 1993, reaching a Yugoslav Cup final, and then managed several other Serbian teams, including OFK Beograd and his native Partizan, that, during his period at the helm, scored 111 goals in a single season, a club record. Won over FC Flora Estonia 6:0, 4:1, won over FC Rijeka Croatia 3:1, 3:0 in UEFA Cup.
In May 2006 he became the coach of FK Partizan, Belgrade for the second time in his coaching career. However, following a disappointing first half of the season, he left the club in January 2007. Since November 2007 he was coaching Litex Lovech. With him Litex won Bulgarian national Cup.
In June 2008, he signed with Romanian Liga I debutant team CS Otopeni and following a series of defeats his agreement was terminated early on 18 August 2008.
On 24 June 2012, he was named as Saudi Professional League side Najran's new head coach. On 7 January 2013, Ješić was reappointed as CSKA Sofia manager, replacing Stoycho Mladenov, but was surprisingly released from his duties on 11 March 2013, after just two games in charge of the team, one of which was won.