Zboril was selected by the Boston Bruins with the No. 13 pick in the 2015 NHL Draft. He was the first of Boston's three straight first-round picks (Jake DeBrusk, No. 14; Zach Senyshyn, No. 15).
The native of Brno, Czech Republic, played three seasons for Saint John of the Quebec Major Junior Hockey League, where he totaled 94 points (28 goals, 66 assists) in 144 games and was named to the 2014-15 QMJHL All-Rookie Team.
During his first season with Providence of the American Hockey League in 2017-18, the left-shot defenseman had 19 points (four goals, 15 assists) and was plus-12 in 68 games.