Her first major role was in three seasons of the Israeli sci-fi TV series Ha'i (English: The Island, 2007–09), which established her popularity among Israel's teenage audiences. She gained recognition for her debut film role in the first Israeli horror film Rabies (Hebrew: כלבת, translit. Kalevet, 2010), which participated in the Tribeca Film Festival, and a number of other venues internationally. Through 2010–11 Grobglas performed a number of lead and supporting roles in prime time Israeli television shows, including in the sitcom Ha-Shualim (English: The Foxes 2010), Ramzor (English: Traffic Light, Hebrew: רמזור), and Hatzuya (2011) (English: Split, Hebrew: חצויה). Grobglas is also known for her role as "The Girl" in the interactive video of We the Kings "Say You Like Me". and as Gabi in the popular Israeli series Tanuhi (Hebrew: תנוחי, English: Relax, 2012). It was announced on 22 February 2013 that the actress was cast in the lead role of "America Singer" in The CW's second pilot for The Selection, though that was ultimately not picked up as a television series. That same year, Grobglas was cast for The CW's's Reign as Olivia, an Italian born noblewoman who is an old flame of Prince Francis (Toby Regbo).