Laviolette, though, said other returning players, likely Kaapo Kakko and potentially rookie Brennan Othmann, will get a chance to play with Kreider and Zibanejad in training camp.
"There are a lot of things I'm familiar with and I have a comfort level with, and then there are things we will see if we can find some chemistry with through different avenues," Laviolette said. "It's hard to give an exact answer and say this is locked in. You'd like to say that, but you've got to go through training camp, get some practices and play some games."
The Rangers signed Carrick to a one-year, $1 million contract July 1 to replace Barclay Goodrow, who was waived with three years remaining on his contract ($3.64 million average annual value) and subsequently claimed by the San Jose Sharks.
Carrick had 16 points (10 goals, six assists) in 77 games combined with the Anaheim Ducks and Edmonton Oilers last season. He had one assist in 10 Stanley Cup Playoff games for the Oilers, who lost to Florida in the Stanley Cup Final.
Carrick is expected to be New York's fourth-line center. He should be on the penalty kill too.
"He brings some grit, sandpaper, face-offs, some physicality," Laviolette said of Carrick. "It's tough losing Barclay, but we replaced him with a character person that bangs bodies, will hit and fight for his teammates, chip in some offense and play some good defense."
Zac Jones is the favorite to replace Erik Gustafsson (signed with the Detroit Red Wings) in the top six defense group that still includes Adam Fox, Ryan Lindgren, K'Andre Miller, Braden Schneider and Jacob Trouba. Chad Ruhwedelis also still in the mix.
Jones played sparingly last season (31 games). He had nine points (two goals, seven assists), but left an impression.
"Zac Jones got better every single time he played for us," Laviolette said. "He had to bring that out in himself every time we called his number, and it wasn't on a consistent basis. When he got the opportunity, he was fantastic. Certainly, he's going to get a long look in training camp."
The Rangers are hoping Panarin, Vincent Trocheck and Alexis Lafreniere can quickly find the same chemistry they had last season, when they formed New York's best forward line and combined for 254 points, including 178 at even strength.
Laviolette said he wants Kakko to assert himself more in the offense. Kakko, the No. 2 pick in the 2019 NHL Draft, had 19 points (13 goals, six assists) in 61 games last season.
Filip Chytil is expected to return to training camp healthy and as the No. 3 center after a full offseason of training.
Matt Rempe has the inside track to be in the opening night lineup, but the Rangers are looking for Othmann, Adam Edstrom and Brett Berard to make enough noise in training camp to potentially force their way into NHL jobs to start the season too.
"This group will be new," Laviolette said. "Even though there are a lot of familiar faces, and a lot of the coaches will be the same, there is change in some of these places and we have to look to build it again, look to get better from where we were last year."