Career
A product of Sloboda Tuzla academy, Bekić had his professional debut on 14 November 2007 playing 20 minutes in a Premier League of Bosnia and Herzegovina match against Velež Mostar. However, Bekić spent the following couple of years mainly playing at youth level before finally establishing himself as a first-team regular in the 2009-2010 season, in which he appeared in 24 league matches and scored 1 goal for the Bosnian side. In July 2010 Bekić was picked up by the Croatian powerhouse Dinamo Zagreb for a fee of 100,000 euros.
At half-season in 2012 Almir returned to Sloboda Tuzla, where he scored 3 goals.
But in this season Sloboda relegated to Prva Liga FBiH, Dinamo sent Bekić on loan to NK GOŠK Gabela. He scored 4 goals and added 5 assist yet.
Bekić was also capped for the Bosnia and Herzegovina U21 side.