Maksimović played youth football in the Džaja football school in his hometown of Banja Luka. His professional career started at another Banja Luka club - FK Borac. He is considered to have been a very creative and hard-working midfielder which secured him a place in the Bosnia and Herzegovina U21 national team.
Maksimović signed with Sarajevo in July 2007. He scored his first goal for the team against Marsaxlokk in the UEFA Champions League qualifiers on 18 July 2007. Afterwards, he played six months with Leotar before returning to Borac in January 2009, and retiring there three years later in 2012.
Maksimović started off his managerial career at BSK Banja Luka in 2015, staying there until 2017. He was then caretaker manager of Borac Banja Luka for one game in March 2018.[2]
On 26 December 2020, Maksimović came back to Borac, this time as a permanent manager, replacing Vlado Jagodić.[3] In his first game as manager, Borac beat Olimpik in a league match on 27 February 2021.[4] Maksimović oversaw his first loss as manager in a league game against Velež Mostar, played on 5 March 2021.[5] In the end however, he managed to guide Borac to a Bosnian Premier League title one game before the end of the 2020–21 season, their first after 10 years.[6] Maksimović also almost guided the club to a 2020–21 Bosnian Cup victory, but lost to Sarajevo in the final.[7] He resigned as Borac's manager on 28 July 2021 after a poor start to the 2021–22 season.[8]
On 16 September 2022, Maksimović was appointed the new manager of Leotar.[9] His first match saw Leotar draw against Sloboda Tuzla on 18 September.[10] On 8 October 2022, he recorded his first win as the club's manager, beating Sloga Doboj 4–1 in a league game.[11] Leotar finished in 11th place in the Bosnian Premier League and were relegated to the First League of RS.[12] On 10 July 2023, Maksimović left the club by mutual consent.[13]
On 26 July 2024, Sloboda Tuzla announced Maksimović as the club's new manager.[14] In his first game in charge, Sloboda lost to Sarajevo 3–1 away on 4 August 2024.[15] With Sloboda sitting in the relegation zone with two points from their previous eight games, Maksimović was sacked as manager on 28 September 2024.[16]