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 on February 3, 2018, against the New Jersey Devils. Zach scored his first two NHL goals on February 13, 2018, against the Ottawa Senators.