[2] Born in Serbia, she moved to Vancouver, British Columbia, with her family during the Yugoslav Wars.
[3] She studied film at Simon Fraser University, and has stated that her experience as an immigrant, living as an outsider in an unfamiliar new society, has informed her creative perspective.
[3] She made several short films, including How I Almost Became a Canadian (2009), Our Little Secret (2011),[4] Maria's Episode (2014) and Cleo (2016),[5] prior to Easy Land, which premiered at the 2019 Toronto International Film Festival.
[6] Her second feature film, Cat's Cry, went into production in 2023.
[7] It premiered at the 2024 Vancouver International Film Festival,[8] where Živković received an honorable mention for the Emerging Canadian Director award.