Growing up, Nardella attended Rosemont Elementary School and East Leyden High School before graduating from East High School. After his freshman year of high school, Nardella decided to drop baseball, basketball and golf to focus on hockey. Nardella played for the Chicago Mission Midget Minor during the 2011–12 season. He began the following season with the team but was unable to compete in the 2013 USA Hockey National Championships after suffering a knee injury in October.
USHL
Nardella was drafted eighth overall in the 2012 USHL Futures Draft by the Sioux City Musketeers. During his rookie season with the Musketeers, he recorded 13 points in 52 games. After impressing scouts during the season, Nardella committed to play collegiate hockey with the Notre Dame Fighting Irish after the 2014-15 season. He was subsequently traded to the Tri-City Storm where he had a breakout season, recording 10 goals and 32 assists to rank third amongst defenseman. As a result, he was selected for the 2014-15 All-USHL Second Team.
Collegiate
In his rookie season at Notre Dame, Nardella broke-out onto the collegiate scene tying fifth most points scored overall on the team and was ranked 13th for points-per-game nationally. As a result, he was named the teams Rookie of the Year following the conclusion of the season. He was selected to participate in the Columbus Blue Jackets Development Camp that summer. In his sophomore season, Nardella helped the Irish participate in the 2017 Frozen Four. At the end of the season, Nardella was invited to participate in the Pittsburgh Penguins Development Camp. During the 2017–18 academic year, Nardella helped the Irish participate in the 2018 National Championship, only to lose to Minnesota–Duluth. After his junior season, Nardella was invited to the Vegas Golden Knights Development Camp. In his senior year with the Irish, Nardella became the 54th player in program history to record 100 points as he reached a new career high. He finished his last year with the team ranking seventh in scoring among defensemen with 23 goals and 77 assists. Due to his successful season, he was selected for the All-Big Ten First Team and earned Second Team CCM/AHCA All-America honors.
Professional
On April 5, 2019, Nardella signed a two-year entry-level contract with the Washington Capitals of the National Hockey League. A few days later, he signed an amateur tryout agreement with the Capitals American Hockey League affiliate, the Hershey Bears. He competed with the Capitals during their 2019 Pre-season games. He recorded his first career AHL goal on December 15, 2019, against the Lehigh Valley Phantoms.
