Stempniak, 32, was in his first season with the Rangers. In 53 games, he had 18 points (nine goals, nine assists) in a career-low average of 12:26 minutes on the ice per game. His $900,000 contract expires after this season.
The Jets are Stempniak's seventh NHL team over his 10-year career.
Klingberg, 24, is a prospect who has appeared in two of his 12 career NHL games this season with the Jets. A 2009 NHL draft pick by the Atlanta Thrashers, Klingberg spent the past three seasons with the Jets and the St. John's IceCaps of the American Hockey League.
- Mike Fiammetta