Sustr left his hometown of Plzen, Czech Republic, at 18 for Kenai River, Alaska, with a stop in the North American Hockey League before joining Youngstown of the United States Hockey League. Sustr accepted a scholarship to the University of Nebraska-Omaha in 2010-11 at age 20. Sustr continued to improve his skating while adding muscle. His strong hockey sense and growing feel for the game at each level of play drew the notice of scouts. By his junior season, Sustr attracted the attention of NHL teams eager to sign the 6-foot-7, 220-pound defenseman, who finished his collegiate career with 15 goals and 51 points in 111 games and earned All-Western Collegiate Hockey Association honors after his junior year. He signed with Tampa Bay on March 21, 2013 and embarked on his pro journey, appearing in two games with the Lightning before being assigned to Syracuse of the American Hockey League. Sustr proved to be a valuable addition to Syracuse on its run to the Calder Cup Finals. Sustr soon became a mainstay for the Lightning, leading him to sign in July of 2018 with the Anaheim Ducks. Currently Andrej plays for Tampa Bay.