Klimchuk, 23, has totaled five goals and five assists for 10 points in 30 AHL games between Stockton and Toronto this season. He was acquired by the Maple Leafs from Calgary on Nov. 28 in exchange for Andrew Nielsen.
A fourth-year pro, Klimchuk has totaled 46 goals and 56 assists for 102 points in 217 career AHL games with Toronto, Stockton and Abbotsford. He was a first-round selection (28th overall) by the Flames in the 2013 NHL Draft and has played one career NHL game.
Gagne, 22, has four goals and five assists for nine points in 33 AHL games with Belleville this season.
A 20-goal scorer and an AHL All-Star in 2017-18, Gagne has collected 26 goals and 14 assists for 40 points in 142 AHL games over three pro seasons with Belleville and Binghamton.
Gagne was a second-round choice (36th overall) by Ottawa in the 2015 NHL Draft.