Marić began his career in for Post SV Wien in 2002. In 2004, at the age of eight, he joined the Rapid Wien youth ranks. Marić was promoted to Rapid Wien II for the 2011–12 season. He made his professional debut on 4 May 2012, getting the start for Rapid Wien II in a 4–0 win over SV Mattersburg II in Regionalliga Ost match He made the match day squad 12 other times that season. The 2012–13 season saw Marić make 9 appearances for Rapid Wien II. He also made the match day squad for the Rapid Wien first team 3 times during the season, but did not appear in a match. On 11 May, 2014 Marić made his first team debut in a 5–2 win over SV Ried in the final Austrian Bundesliga match of the season. He also made 7 appearances with Rapid Wien II during the season. He made his first appearance of the 2014–15 season on 14 February 2015, a 3–0 win over SV Ried. Marić served primarily as the second choice goalkeeper for the season, making 7 league appearances and one in the Austrian Cup while making the bench for 21 other times. He also made 9 appearances for the second team during the season. On 19 June 2015, it was announced that Marić would be leaving Rapid Wien after he was unwilling to sign a contract extension.
Marić signed with German Bundesliga club TSG 1899 Hoffenheim on 30 June 2015. He was immediately loaned to Polish Ekstraklasa club Lechia Gdańsk for the 2015–16 season. On 17 July 2015 he made his debut for Lechia in a 1–0 defeat to KS Cracovia in the opening match of the Ekstraklasa season. He started the first 23 league games of the year for Lechia before losing the starting job to Vanja Milinković-Savić. Marić made 24 league appearances and one appearance in the Polish Cup for Lechia, keeping 7 clean sheets.
On 31 January2017 Marić was sent on loan to Hannover 96, who were playing in the 2. Bundesliga. However, he would not make any appearances with the Hannover first team, rather spending time with Hannover 96 II in the Regionalliga Nord. Marić made his first appearance for Hannover 96 II on 11 February in a 2–1 loss to SV Eichede. He would make 13 appearances with Hannover 96 II during the loan.
On 1 August 2017, he went on loan to Norwegian Eliteserien club Lillestrøm SK until the end of the 2017 season. Marić made his debut for LSK on 24 August 2017, a 3–0 loss to Rosenborg BK. On 24 November 2017, Marić's loan was extended until 2019. Marić made his first appearance of the 2018 season on 11 March 2018, getting the start in a 3–1 defeat to Bodø/Glimt in the opening match of the season. He made 25 appearances in the Eliteserien as he helped LSK finish in 12th place, 3 points above the relegation zone. Marić also made 5 appearances in the Norwegian Cup to help LSK reach the semifinals, where they lost 3–0 to Strømsgodset Toppfotball. 1 April 2019 Marić made his first appearance of the 2019 season in a 1–1 draw with Stabæk in matchweek 1. He would make 30 starts in the Eliteserien as Lillestrøm finished in 14th place, sending them to the relegation playoffs. Marić played both legs of the playoff matchup with IK Start. LSK won the first leg 2–1, but lost the return leg 4–3, being relegated on away goals. Marić started 34 of the 35 matches for LSK in the 2019 season, the only one he failed to appear in being a Norwegian Cup first round matchup with Gjelleråsen IF
Houston Dynamo
On 13 January 2020, Marić signed with Major League Soccer side Houston Dynamo. On February 29, 2020, Maric made his debut with the Dynamo in a 1-1 draw against LA Galaxy.
International career
Marić played for the Austria U-16 team in a friendly in 2011. In 2012, Marić decided to represent Croatia and filed a one-time switch with FIFA. He would represent Croatia at the U-16, U-17, U-18, and U-19 levels, making 29 appearances for the various Croatian youth national teams. Marić made 3 appearances for Croatia at the 2013 FIFA U-17 World Cup.
