Prior to Notre Dame, Nardella played in 108 games in the USHL between the Sioux City Musketeers and the Tri-City Storm, recording 55 points (11g, 44a) in two seasons. During the 2014-15 season, Nardella, as a member of Tri-City, ranked third among USHL defensemen in points (10g, 32a) and was named to the 2014-15 All-USHL Second Team.
At the international level, Nardella represented Team USA at the 2014-15 World Junior A Challenge, recording two assists en route to a gold medal in Kindersley, Saskatchewan. Additionally, Nardella won a silver medal in the 2013 Ivan Hlinka Tournament held in the Czech Republic and Slovakia. In 2012, as a member of USA Hockey's U-17 team, Nardella won a gold medal at the Five Nation Tournament held in the Czech Republic.
Nardella is the son of Bob Nardella, who appeared in 100 games with the Chicago Wolves in the American Hockey League and represented Italy twice at the Olympic Games (1998: Nagano; 2006: Turin).