Peslarová developed in the minor ice hockey department of HC RT Torax Poruba in her home city of Ostrava, in the eastern Czech Republic. By age 14, she was playing with the HC Poruba men's under-16 (U16) team in the Junior Youth Extraliga (Czech: Extraliga mladšího dorostu, ELMD) and she first played with the HC Poruba men's under-18 (U18) team in the Senior Youth Extraliga (Czech: Extraliga staršího dorostu, ELSD) at age 15.
She made her senior league debut with SK Karviná of the Women's 1st Hockey League (Czech: 1. liga ženského hokeje, shortened to 1. liga žen), the top women's league in the Czech Republic, in the 2011–12 season. She continued to divide her playing time between the HC Poruba men's junior teams and the SK Karviná women's team during the 2012–13 and 2013–14 seasons, never playing more than 20 games in any league per season.
As her 18th birthday approached and she would no longer be eligible to play in Czech men's junior leagues, Peslarová looked abroad to further her development. For the 2014–15 season, she relocated to the Siberian city of Krasnoyarsk to sign with Biryusa Krasnoyarsk of the Russian Women's Hockey League (RWHL; replaced by the Zhenskaya Hockey League in 2015). Another relocation preceded the 2015–16 season, with Peslarová settling in Stockholm to join SDE Hockey of the Riksserien (renamed SDHL in 2016), as the team's starting goaltender.
After two seasons with SDE, Peslarová signed for the 2017–18 season with the men's representative B-team of HC Poruba in the Czech Regional Hockey Championship (Czech: Krajské hokejové přebory, abbreviated to Krajský přebor), the fourth-tier men's ice hockey league in the Czech Republic. During the season, she became the first woman to post a shutout in a Czech men's league, denying all thirteen shots on goal during a match against HK Nový Jičín.[2] In addition to playing with HC Poruba B, she also returned to SK Karviná of the renamed Czech Women's Extraliga (Czech: Extraliga ženského hokeje) for the 2017–18 season.
After one season in the Czech Republic, Peslarová returned to Sweden to sign with her second SDHL club, MoDo Hockey in Örnsköldsvik.[3][4]