After appearing in a number of short films, in 2009, Burge made her television debut as Becky Sproles in the NBC/DirecTV drama Friday Night Lights in the fourth season until the show ended with the fifth season in 2011. According to a local interview, Burge said prior to being cast, she did not watch the show, but that did not limit her abilities when auditioning for the part as she was "so right on" for the role.
Also in 2011, Burge appeared in the horror comedy Humans vs Zombies, based on the live action role-playing game.
In 2012, Burge appeared in the family movie Cowgirls n Angels and actually performed some of the Stunts on horseback.
In 2013, Burge appeared in My Jerusalem's music video "Mono". She also had a recurring role in the eighth and final season of the Showtime crime drama Dexter as Niki Walters, the daughter of Vince Masuka (C.S. Lee).
In 2014, Burge had a recurring role as Zoe in seven episodes of the short-lived CW science fiction romantic drama Star-Crossed, which starred her former Friday Night Lights co-stars Aimee Teegarden and Grey Damon. That same year, she played Dora in the Sasquach horror film Exists directed by Eduardo Sánchez.
In 2015, Burge joined the cast of the NBC drama Chicago Fire, replacing Charlie Barnett who played Peter Mills as Jessica "Chili" Chilton, the paramedic in charge in the third season. Burge was added to the main cast in the fourth season. In 2016, her character was written out of the show.
In 2017, she appeared in the Viceland series What Would Diplo Do? opposite James Van Der Beek.
