In his playing career Adžem was a full-back. It is said that he was a very strong player and that it was really hard to get pass him. Adžem played for a number clubs. He played for hometown club Željezničar on 4 occasions, Zagreb, Đerzelez, Pogoń Szczecin, GKS Katowice and Zagłębie Sosnowiec where he finished his career. Adžem played in 104 league games and scored 6 career league goals for Željezničar, with whom he won all of his trophies. While playing for Željezničar he won the Bosnian Premier League 2 times, in the seasons 2000–01 and 2001–02, the Bosnian Cup 1 time, in the 2000–01 cup season, the same year that Željezničar completed the double. He also won the Bosnian Supercup 3 times, in 1998, 2000 and in 2001. For all the other clubs, Adžem made 114 league appearances and scored 1 goal while playing for Katowice, thus in total playing 228 league games and scoring 7 league goals in his career. He finished his career in 2007 while playing for Zagłębie Sosnowiec at the age of 34.
On 6 June 2014, Adžem was named new manager of Željezničar replacing Hajrudin "Dino" Đurbuzović who was sacked earlier in the day. In 22 games Adžem amassed an impressive record of 11 wins, 7 draws and only 4 losses. On 15 December 2014, Adžem had to be removed from the position of manager due to not having an UEFA Pro Licence to manage a first team of any club. He went back to coach in the club's Youth School while also working on to finish getting his license.
Željezničar U19
Adžem managed a junior side of Željezničar from January 2015 to July 2017 with whom he won the Bosnian league title twice. First time in the 2014–15 season and the second time in the 2016–17 season.
Return to the Željezničar (first team)
On 23 July 2017, Adžem came back to the position of manager of Željezničar's first team after almost 3 years of his first appointment. In that season Adžem won the club's first trophy in 5 years after beating Krupa in the two legged final of the 2017–18 Bosnian Cup. In the first game, Željezničar beat Krupa 2–0 and in the second game 4–2. He also could have won the double since Željezničar was for the majority of the season first in the league, but eventually finished on second place after a poor finish to the season. Before the start of the pre-season, on 4 June 2018, Adžem got sacked.
Željezničar U17
In July 2019, Adžem became the new manager of the under-17 team of Željezničar. In his first match as the U17 team manager, Adžem's team beat the Borac Banja Luka U17 team on 20 July 2019 at home, with the result being 2–0 for Željezničar. Adžem's first loss as the under-17 manager came on 3 August 2019, in a 1–0 away league loss against the under-17 team of Zrinjski Mostar.
