Adžem made his senior debut for Bosnia and Herzegovina in a February 1997 friendly match against Vietnam and has earned a total of 14 caps, scoring 1 goal.
[1] On 6 June 2014, Adžem was named new manager of Željezničar first team, replacing Dino Đurbuzović who was sacked earlier in the day.
[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.
[14] On 17 September 2020, it was confirmed that Adžem had become the new youth coach of UAE Pro League club Al Wasl.
[17] On 13 February 2024, Goražde announced that Adžem would depart the club for Bosnian Premier League side GOŠK Gabela.
[18] On 13 February 2024, Adžem was appointed the new manager of GOŠK Gabela on a one-and-a-half-year deal, replacing Toni Karačić.
[23] On 28 August 2024, First League of FBiH side Jedinstvo Bihać announced the appointment of Adžem as its new manager.