She specializes in the giant slalom and started her first European Cup race at age 15 on February 24, 2001, in Rogla, Slovenia.

In season 2016 she finished as seventh in giant slalom ranking, achieving two podiums in World Cup, the first of her career.

[1] Ranked among the greatest Slovenian giant slalom skiers, Drev's career was plagued by health problems and instability in her national team, which didn't allow her to live up to her potentiality.

Drev started the 2015–16 FIS Alpine Ski World Cup well, leading in the giant slalom, before Lara Gut and Eva-Maria Brem, by the end of December, after performing "sensationally" in Lienz.

Drev expressed regret at not having lived up to her potentiality, stating that she was especially disappointed with her results at the 2018 Winter Olympics in Pyongyang, where she felt she could get a medal.