[2] She currently plays lead on the Czech national women's curling team, skipped by Anna Kubešková.

The team won their tie-breaker match against Denmark's Stephanie Risdal Nielsen before losing to Russia's Yulia Portunova in the playoffs.

After returning form Canadas Championship her team lost Czech Nationals and could not represent the country is season 2014/2015.

In 2016 they played in the 2016 Europeans and finished in 4th place losing to the Swedish team skippered by Anna Hasselborg in the Semi finals, which also qualified them for the 2017 World Women's Curling Championship in Beijing.

After round robin Svatoňová and her team with Anna Kubešková as skip, Alžběta Baudyšová as third, Tereza Plíšková as second, Ezhen Kolchevskaia as alternate and coach Karel Kubeška, finished fourth and did not get chance to fight for top two places.

In March 2018 they improved Czech current best placement and finished 6th on Worlds in Canada losing Russia in play-offs (Victoria Moiseeva) with 6–6 record.