Kane has a lengthy suspension history, including 3 games for this elbow on Neal Pionk in 2020.
Given the fact that his most recent suspension for an on ice incident (his 21 game suspension for Submitting a fake proof of vaccination will not be counted) Kane will not be considered a repeat offender in this case.
Kadri, at this point, is expected to be out at least until the end of the Western Conference Finals. As such, if the Department of Player Safety has any interest in keeping things fair, Kane shouldn't play another game in this series either. There is precedent here. Kadri himself was suspended for the remainder of the series after cross checking Boston's Jake Debrusk in the first round of the 2019 playoffs. The NHL did not specify whether the hearing would be done in person or over the phone, so at this point, it's impossible to say what sort of punishment George Parros has in mind.