*Club domestic league appearances and goals, correct as of 11:01, 22 September 2024 (UTC) ‡ National team caps and goals, correct as of 19:46, 18 June 2021 (UTC)
Čelůstka began his career with Fastav Zlín, making his professional debut in the Czech First League during the 2007–08 season, and then playing more regularly in the following one.[3] His good performances ensured him a regular place with Czech leading club Slavia Prague, with whom he made fourteen appearances and a goal in the first half of the 2009–10 Czech First League.[2]
On 1 February 2010, Čelůstka signed with Serie A outfit U.S. Città di Palermo on loan, with an option to sign him permanently at the end of season.[4] He was awarded the number #89 jersey from the rosanero.[5] He made his league Serie A debut in 2010, coming as a substitute for Marco Calderoni in the second half during a 3–1 home victory against Bologna.[6]
Trabzonspor
On 8 July 2011, Čelůstka moved to Turkish club Trabzonspor for a transfer fee of €900,000[7] and signed a five-year contract.[8][9] The club gave him the number 28 jersey.[10]
Čelůstka represented the various Czech Republic youth football teams that ranged from U19 until U21. His performances at the 2011 UEFA European Under-21 Football Championship saw him named in the Team of the Tournament. On 15 November 2013, he debuted for the senior team in a 2–0 victory against Canada, scored after just three minutes.[18]