[11] Kim joined semi-professional club Gyeongju KHNP on 1 July 2016, and participated in the Korea National League from the middle of the 2016 season.

[15] Jeonbuk manager Choi Kang-hee expressed his expectancy about him during the pre-season training camps in Dubai,[16] and used him as a key player from the beginning.

[24] Kim scored his first goal of the 2018 season with a header as well as showing strong defense in a K League 1 match against FC Seoul on 18 March, and was named the MVP of the week.

[29] At a similar time, he received intensive attention from a wide range of European clubs,[30][31] and Tottenham Hotspur manager José Mourinho tried to recruit him.

Two days after receiving his first red card in the Süper Lig against Trabzonspor on 17 October,[35] Kim said "This was a first for me in my five-year career playing football at the highest level, I guess we have to have such experiences in Turkey.

[39][40][41] On 27 July 2022, Kim signed for Serie A club Napoli[42] for a reported fee of €18 million,[43] as a replacement for Kalidou Koulibaly, who departed to join Chelsea.

[55] In the first half of the 2023–24 season, he was selected for Bundesliga's Best XI by fans,[56] but magazine kicker criticised his inconsistent performance including his mistakes against Saarbrücken, which eliminated Bayern from the DFB-Pokal.

[57] During the second half of the season, he frequently allowed the space behind him due to his inaccurate decisions,[58] and manager Thomas Tuchel preferred Eric Dier and Matthijs de Ligt after pointing out that he did not follow the promised tactics.

[59][60] Kim disappointed Bayern management as he made an error followed by one of VfL Wolfsburg's goals in the first game of the 2024–25 Bundesliga,[61][62] but kept seven consecutive clean sheets between October and November 2024, with his ability improved under new coach Vincent Kompany.

[65] In said tournament against Iran on 31 August 2017, Kim debuted as a starter and sent off Iranian footballer Saeid Ezatolahi while showing great defense for 84 minutes.

As a result of this victory, Kim and his teammates received an exemption from military service, reducing the two-year conscription to just a few weeks of basic training,[69] which he later served in the summer of 2023.

[71] He helped his team keep clean sheet against Uruguay, but was criticized for his performances against Ghana and Brazil, with the latter eliminating South Korea in round of 16, following a 4–1 defeat.

His long pass accuracy enables him to immediately hit the ball after the steal to complete a quick counterattack, and his excellent aerial ability and positioning allows him to perform headers to break up opposition attacks and start offensive plays.

Despite his tendency to stay back, Kim exhibits a proactive and aggressive approach in winning possession beyond his defensive line.