For the moment, the only thing we know is that Lightning GM Julien BriseBois sent multiple first round picks to Chicago for Hagel. It seems like a very steep price, but Hagel is signed until the 2023-24 season at a very cheap 1.5 M$ annual salary. Don't forget that he has 21 goals and 16 assists this year with the Blackhawks in 55 games.
Here's the full trade : the Chicago Blackhawks trades Brandon Hagel, two fourth round picks (in 2022 and 2024) for two first round picks (in 2023 and 2024), Tyler Raddysh and Boris Katchouk.