Early career He is a product of the
Yunist Chernihiv where he started his football career, before moving to
Desna-2 Chernihiv. In 2019 Tatarenko was listed as a third goalie of
Desna Chernihiv, but he did not get much of playtime partially due to his young age.
Kudrivka After a season he moved to
Kudrivka where in 2020 won the
Kyiv Oblast Football Federation and in 2011 the
Kyiv Oblast Football Cup and
Chernihiv Oblast Football Cup and the Chernihiv Oblast Super Cup.
Druzhba Myrivka In January 2023 he signed for
Druzhba Myrivka, where he won the
Ukrainian Amateur Cup and the
2023–24 Ukrainian Second League.
FC Chernihiv On 21 June 2024, he joined to
Chernihiv in
Ukrainian Second League. He soon surpassed Oleksandr Shyray as the club's starting goalkeeper. he made his debut in the
2024–25 Ukrainian Cup against
Chaika. On 12 August, he saved a penalty by
Serhiy Mashtalir against
Viktoriya Sumy in Ukrainian Cup. In September, he was elected player of the month in Ukrainian Second League. By 26 May 2025, Maksym had kept 291 minutes of clean sheets since the start of the season, which was a single-season record for the league. Tatarenko imposed himself as the best goalkeeper Ukrainian Second League, finishing the 18 matches-long season conceding only 8 goals, helping
FC Chernihiv obtain Ukrainian First League promotion during the
2024–25 Ukrainian Second League. On 26 June 2025, even if few clubs in Ukrainia Premier League were interested, he decided to extend his contract with the club. He made his
Ukrainian First League debut with FC Chernihiv on 3 August 2025, in a 1–0 away lost with
Probiy Horodenka. On 17 August, during the match against
Prykarpattia Ivano-Frankivsk, he kepts a clean sheet for the first time in the Ukrainian First League. Tatarenko played FC Chernihiv's matches in the Ukrainian Cup, impressing enough helping the club to qualify for the round of 16 for the first time. Due to his performance in the match against
Vorskla Poltava, he was included in the Best XI of Round 10 of the
2025–26 Ukrainian First League. ==Career statistics==