As a player with the Middlebury Panthers women's ice hockey program, Hlinka recorded 20 goals and 45 assists for a total of 65 points in 113 career NCAA Division III games. She and future Whale teammate Emily Fluke were Panther teammates for one season.[2]
Hlinka relocated to Europe after graduating from college. During the 2018–19 campaign, she suited up for ŠKP Bratislava U16 in the Liga kadetov, the top under-16 (U16) boys' league in Slovakia, posting 12 goals and 11 assists in 21 games. She then spent two seasons with Skellefteå AIK in the Swedish Damettan, where she led the team in scoring both seasons. She tallied 25 points (14+11) in 21 games over the span.
Hlinka represented Slovakia in the Division I Group A tournaments of the IIHF Women's World Championship in 2019, 2022, and 2023.[3] She led the team in goals at the 2019 tournament, notching two across five games played.[4]
She ranked second in scoring of all tournament skaters at the 2024 IIHF Women's World Championship Division I Group B, with 3 goals and 5 assists for 8 points in five games.[5] Her performance was recognized with selection as the best forward of the tournament by the tournament directorate and as best player for Slovakia by the coaches.[6][7]