Adžem played in 104 league games and scored six career league goals for Željezničar, with whom he won all of his trophies. While playing for Željezničar he won the Bosnian Premier League twice, in the seasons 2000–01 and 2001–02, the Bosnian Cup once, in the 2000–01 cup season, the same year that Željezničar completed the double. He also won the Bosnian Supercup three times.
Adžem 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 first team, replacing Dino Đurbuzović who was sacked earlier in the day.[2] In 22 games, he amassed an impressive record of 11 wins, 7 draws and only 4 losses.[3]
On 15 December 2014, Adžem had to be sacked 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 obtaining his license.[4]
Željezničar (youth)
Adžem coached the under-19 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.[5][6]
In July 2019, Adžem became the new manager of the under-17 team of Željezničar.[7] In his first match as the U17 team manager, his side beat the Borac Banja Luka U17 team on 20 July 2019.[8] Adžem's first loss as the under-17 manager came on 3 August 2019, in a 1–0 away loss to the under-17 team of Zrinjski Mostar.[9] On 27 July 2020, he left the under-17 team of Željezničar.[10]
Return to Željezničar
On 23 July 2017, Adžem came back to the position of manager of Željezničar after almost 3 years of his first appointment.[11]
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.[12] He also could have won the double since Željezničar was for the majority of the season first in the league, but eventually finished in second place after a poor finish to the season.[13]
Before the start of the pre-season, on 4 June 2018, Adžem was sacked.[14]
Al Wasl (youth)
On 17 September 2020, it was confirmed that Adžem had become the new youth coach of UAE Pro League club Al Wasl.[15]
On 13 February 2024, Adžem was appointed the new manager of GOŠK Gabela on a one-and-a-half-year deal, replacing Toni Karačić.[19] On his debut four days later, the team beat Igman Konjic 2–1 away from home.[20] On 23 February, Adžem suffered his first defeat as GOŠK manager in a 4–2 home loss to Sloga Meridian.[21] He finished the season with GOŠK in ninth place, avoiding relegation.[22]
After opening the 2024–25 season with two defeats, Adžem was sacked as manager on 12 August 2024.[23]
Jedinstvo Bihać
On 28 August 2024, First League of FBiH side Jedinstvo Bihać announced the appointment of Adžem as its new manager.[24] He debuted as manager in a 1–0 loss to his former club Goražde on 31 August.[25]