At age four, Frederik joined a chess club and began learning and playing against Rasmus.

[3] In April 2021, Svane, then a FIDE Master, defeated Matthias Blübaum (then the top-rated German player) in a surprise upset in the Kader Challenge, a tournament for top-level German chess players.

[3] In October 2021, Svane achieved his first GM norm by finishing in second place at a round-robin in Kiel, Germany.

[2] In May 2022, he obtained two GM norms in less than one day by finishing second in a closed GM tournament held by the Hamburg Chess Club with a performance rating of 2607, and then drawing against Eduardas Rozentalis in the Hamburg Invitational.

At his Chess Olympiad debut in 2024, he earned an individual gold medal, scoring 8/9 on board five.