Plazonja started his football career with Cibalia at the age of 14 before moving to Osijek in 2013. After spending 5 years with Osijek, Plazonja was rewarded with a move to Croatian giants Dinamo Zagreb on 20 February 2017 spending most of the times in the team academy.
On 4 September 2017, Plazonja signed his first professional contract with Slovenian club Koper. He make his debut on 6 September coming on as a substitute during the 2017–18 Slovenian Football Cup Round of 16 tie against Triglav Kranj.
On 10 August 2018, Plazonja moved back to Croatia to signed for Kustošija. In his second game for the club on 31 August, he scored his first professional career goal scoring the third goal for the team in a 3–2 win over Dugopolje. On 20 October, Plazonja scored the winning goal in the 79th minute in a 2–1 league win over Međimurje.
On 5 September 2019, Plazonja signed with Romanian club Hermannstadt. He make his debut on 21 September in a goaless draw against Sepsi OSK.
Plazonja then moved on loan to Șelimbăr on 12 February 2020 until the end of the season on 30 June 2020.
Plazonja was then loan to second division club Politehnica Timișoara on 27 August 2020.[1][2] He went on to score 4 goals in 28 appearance in all competition for the club.
On 29 January 2022, Plazonja signed for Romania club, Concordia Chiajna. He was released by the club on 31 July after making 13 appearances for the club.
On 14 September 2022, Plazonja returned to Croatia to signed for Bijelo Brdo. He went on to scored on his debut Solin in a 2–1 league win on 24 September.
On 7 July 2023, Plazonja joined the Rudeš.[3] He make his club debut against Osijek on 30 July in a 3–4 lost.
On 8 September 2023, Plazonja signed for Bosnian club Široki Brijeg on a 2 years contract. However, he was released 6 months into his contract.[4][5]
On 9 March 2024, Plazonja moved to Southeast Asia to signed with Singapore Premier League club Hougang United for the 2024–25 season. On 10 May 2024, he made his club debut in a 4–1 defeat to Lion City Sailors. He would then go on to make his second league appearance in a 1–0 defeat to Albirex Niigata (S) but was subbed out as he sustained a hamstring injury which made him unavailable for the club third league match against Tanjong Pagar United. On 14 June 2024, he returned from injury and was subbed on for Justin Hui, where he recorded his first league goal and assist in a 2–6 defeat to rival club Geylang International.[6] On 11 August 2024, he won a man of the match award in a 5–1 win against Tanjong Pagar United, where he recorded two goals and two assists. Plazonja clocked in an incredible 36.90 km/h tying with former Real Madrid and Wales international footballer, Gareth Bale as the second world's fastest player ahead of world renowned footballer Kylian Mbappé at 36.70 km/h and behind Tottenham Hotspurs player, Micky van de Ven at 37.38 km/h in a 1–0 win over the Eagles.[7]