Gallant replaced David Quinn as Rangers coach June 16 after they finished fifth in the eight-team MassMutual East Division (27-23-6) and failed to qualify for the Stanley Cup Playoffs.
The 58-year-old is 270-216-51 with four ties for the Columbus Blue Jackets, Florida Panthers and Vegas Golden Knights. He's 18-15 in 33 playoff games, including leading the Golden Knights to the Stanley Cup Final in their inaugural season of 2017-18.
"When I was in Vegas, we went into training camp with a plan, we put our systems in place and we expected everybody to play a 200-foot game," Gallant said in June. "Everybody good defensively, everybody good offensively, everybody to handle a role on the hockey team. That's what's important for me.
"It's not going to take 15 guys to win, it's going to take 23 guys on your roster to win games every night. I will try to make every player important to our hockey team. Everybody has a role to play, and that's what we expect."