Sedláček qualified for the 2014 BDO World Darts Championship playing Paul Hogan in the preliminary round, losing 3–1. He qualified for the 2014 BDO World Trophy, won in the first round 6–1 over Robbie Green, then lost in the last 16 to Paul Jennings 7–2. He qualified for the 2015 BDO World Darts Championship, playing Paul Coughlin in the preliminary round; he won 3–2. He lost to Glen Durrant 3–1 in the first round, despite having the highest average, 99.58, of all the first round matches, and the third-highest losing average in Lakeside history.
Sedláček was also able to qualify for his home tournament, the 2019 Czech Darts Open, where he was eventually beaten in the second round 6–4 by Ian White.
On 18 January 2020, he beat Berry van Peer in the final of Day Three at European Q-School to win a PDC Tour Card for the first time, making him the first Czech player to earn a Tour Card.[6]
At the 2021 UK Open, Sedláček won 6–0 against Rhys Griffin but was then eliminated by Simon Whitlock 10–7. On the PDC Pro Tour, Sedláček reached at most the last 16 whereupon he lost his Tour Card and had to go back to 2022 Q-School. As a former Tour Card holder he started in the final stage, but he didn't win his Tour Card back.[7]
Sedláček regained his PDC Tour Card at 2023 Q-School, finishing 6th on the European Order of Merit.[10]
In 2024 Sedláček made it to the quarter-finals at a Players Championship event for the first time at Players Championship 6 in Hildesheim and made it to the semi-finals at Players Championship 16 in Milton Keynes. These results helped him qualify for the 2024 Players Championship Finals as the 43rd seed, where he lost to 22nd seed Ryan Joyce 6–4 in the first round. After a one year absence, Sedláček also qualified for the 2025 PDC World Championship, where he was trying to secure his Tour Card by finishing the season in the top 65 on the PDC Order of Merit. However, he lost to debutant Rhys Griffin 3–0 in sets in the first round and due to the results of Robert Owen, Nick Kenny and Jeffrey de Graaf, he dropped to 66th place on the rankings and lost his Tour Card.[11]