The women's team has been playing in the Extraliga žen ve florbale (the highest competition) since the 2023–24 season, to which they advanced for the first time in history in 2023.

[3][4] Among the team's greatest successes is the promotion to the quarterfinals of the Pohár Českého Florbalu in 2022.

[5] The men's A team play in the third highest competition Národní liga, from the 2023–24 season, to which they were first promoted in 2023.

[6] The club was founded in 2011, when in its first ever season it entered a women's team in the 2nd league (the 3rd highest competition in the Czech Republic).

[9] In the 2021–22 season, the men's A team successfully managed to rebuild the squad, which included players from junior and adolescent teams, this was already evident at the Czech Open tournament, from which Třinec took home silver medals in the Open category.