Kaur made her film debut with a small role in an English film - One Night with the King (2006). Kaur starred in Anurag Kashyap's production Peddlers (2012), her debut hindi film, which was screened at the 2012 Cannes Film Festival, followed by The Lunchbox (2013) with Irrfan Khan, which was screened at the 2013 Cannes Film Festival. In 2015, she starred in Showtime's TV series Homeland playing the role of Tasneem Qureshi, an ISI Agent.