Cuylle finished the regular season with 13 goals, eight assists and 247 hits in 81 appearances.
Brodzinski was a healthy scratch for the last two games of the regular season, and he finished the campaign with six goals and 19 points in 57 appearances.
Rempe was in the lineup for the last two games of the regular season and finished the 2023-24 campaign with one goal, one assist, 50 hits and 71 PIM in 17 appearances.
Shesterkin was the first goalie off the ice at the morning skate, Mollie Walker of the New York Post reports, indicating he will patrol the home crease Monday against Ottawa.
Shesterkin turned aside 34 shots in regulation and overtime and both shootout attempts he faced in Saturday's 3-2 win over the Islanders.
Shesterkin will guard the home net Saturday versus the Islanders, Andrew Gross of Newsday.
Chytil (head) skated with the team Friday after being medically cleared, though he remains without a clear recovery timeline, Darren Dreger of TSN reports.
Panarin scored a goal on four shots in Thursday's 4-1 loss to the Flyers.
Quick will patrol the home crease against Philadelphia on Thursday, Vince Z. Mercogliano of USA Today reports.
Shesterkin will guard the road goal Tuesday against the Islanders, per Vince Z. Mercogliano of USA Today.
Shesterkin will guard the home net Sunday versus Montreal, Colin Stephenson of Newsday reports.
Kreider recorded a power-play goal in Friday's 4-3 win over the Red Wings.
Quick was the first goaltender off the ice at morning skate, Peter Baugh of The Athletic reports, and is slated to patrol the visiting crease in Detroit on Friday.
Fox collected two assists, one on the power play, in Wednesday's 4-3 win over the Devils.
Lafreniere produced a goal and an assist in Wednesday's 4-3 win over the Devils.
Panarin scored an even-strength goal and added a power-play assist in Wednesday's 4-3 win over the Devils.
Shesterkin made 17 saves in Wednesday's 4-3 win over the Devils.
Gustafsson (upper body) is expected to play Wednesday versus the Devils, Vince Z. Mercogliano of USA Today reports.
Shesterkin is expected to start at home against the Devils on Wednesday, per Peter Baugh of The Athletic.
Vaisanen penned a three-year, entry-level contract with the Rangers on Wednesday.
Scanlin was reassigned to AHL Hartford on Tuesday.
Mancini agreed to terms on a two-year, entry-level contract with the Rangers on Tuesday.
Gustafsson (upper body) is not expected to be an option for Monday's matchup against Pittsburgh, per Vince Z. Mercogliano of USA Today.
Shesterkin will be between the pipes at home versus Pittsburgh on Monday, Vince Z. Mercogliano of USA Today reports.
Quick will defend the road net Saturday against Arizona, Mollie Walker of the New York Post reports.