Zary, 25, is in the second year of a three-year deal worth $3.775 million annually. He was a healthy scratch in the Flames’ second game of the season, but returned for the third.
The 2020 first-round pick (24th overall) had 12 goals and 13 assists in 74 games last season, his third full year with the NHL club.
Pachal had one goal and six assists in 39 games for Calgary last season, while Robertson put up six goals and 12 assists in 72 games with New York.
Both Zary and Pachal are headed for the AHL’s Calgary Wranglers.
Pyythia, 24, has played 71 NHL games over three seasons, tallying five goals and six assists. Harkins, 29, appeared in one game for the Lightning this season after posting three goals and five assists in 44 appearances for the Anaheim Ducks last season.