A native of Staten Island, NY, Zach signed a two-year, entry-level contract with the Pittsburgh Penguins on March 14, 2017, after being named Hockey East Player of the Year and a Hobey Baker Award finalist following his senior season at Northeastern University, where he amassed 63 points (31 goals, 32 assists) in 38 games.

He began the 2017-18 season with Wilkes-Barre/Scranton but was called up by the Penguins after the All-Star break and made his NHL debut Feb. 3, 2018, against the New Jersey Devils. Zach scored his first two NHL goals Feb. 13, 2018, against the Ottawa Senators.