Although a talented player, with good technical skills, Amar never managed to match the success or renown of his father, Ivica Osim's playing career.

Osim's managerial career started in Željezničar's youth squad which he guided to success in domestic competitions.

Amar's father Ivica Osim invited him to Japan to be his assistant at JEF United Chiba.

In his first season as manager, Osim immediately guided the club to win the league title and finished as national cup runners-up.

In 2012, he claimed the league title once again, with three rounds left to play, breaking many records on the way and also defended the national cup, bringing the double back to Željezničar after eleven years.

[6] In his second season as the club's manager, Osim's Al Kharaitiyat finished in 12th place, just narrowly missing relegation.

[7] On 31 December 2018, Osim once again came back to Željezničar and signed a three-and-a-half-year contract after monthly speculations of him becoming the manager even earlier.

[21] He also guided the team to the semi-finals of the 2019–20 Bosnian Cup, but did not get the chance to win the competition as it was abandoned due to the pandemic, with no winner being proclaimed.

[23] With three more league wins after the Velež game, Željezničar suffered its first loss under Osim in the new season on 21 August 2020, an unexpected 1–0 home defeat against Mladost Doboj Kakanj.

[24] In Osim's first European game with Željezničar since his return, his team lost 3–1 against Israeli club Maccabi Haifa in the 2020–21 UEFA Europa League first qualifying round on 9 September 2020.

[25] In the middle of an eight-game winless run in the 2020–21 league season, which had culminated with a home draw against Mladost Doboj Kakanj, Osim was sacked by the club on 11 April 2021.

[26] On 11 June 2022, Osim signed a one-year contract with Velež Mostar, with an option to stay at the club even longer.

[27] On 15 July 2022, he took charge for the first time as Velež manager for their Premier League match against Posušje, which ended in a 1–1 draw.

[28] On 28 July, Velež unexpectedly got eliminated from the 2022–23 UEFA Europa Conference League in the second qualifying round by Maltese club Ħamrun Spartans.