On July 24, 2006, Klee signed a one-year contract with the Colorado Avalanche as a free agent for the 2006–07 season.

[3] On September 26, 2008, into the final year of his contract with the Thrashers, Klee was dealt along with Brad Larsen and Chad Painchaud to the Anaheim Ducks for defenseman Mathieu Schneider.

That season, he also guided the U.S. Women's Under-22 Select Team to a first-place finish during his first campaign behind the bench for the U.S. in the 2014 Under-22 Series, defeating Canada in all three games.

Serving in the same capacity at the 2015 Four Nations Cup in Sundsvall, Sweden, Klee led the U.S. to an undefeated record (3–1–0–0) and first championship title since 2012.

The tournament marks the seventh consecutive event that Klee has been at the helm of Team USA and the third time he has been behind the bench at the Four Nations Cup.

Having left the women's national team, on July 18, 2017, Klee was hired as an assistant coach with the Syracuse Crunch of the American Hockey League.