Not that hits are everything, but Liljegren would be 3rd on Calgary's defense in hits behind Weegar and Zadorov... And he was not playing 20+ minutes a night.
Treliving's big thing is more puck moving ability, ability to defend in front of the net, and blocking shots. So I think he will actually like the guys on our defense, including Holl and Schenn. The only big and nasty defenseman he really had last year was Zadorov, and while I think he wants at least one on his defense (which is likely the kind of guy he targets to fill the hole left by Schenn/Holl), he hasn't really had more than two at a time. The rest of his guys are not drastically different than what the Leafs have already.
Liljegren is not quite as thick as Rasmus Andersson is right now, but there are a lot of parallels between their games (especially when you look at Andersson from 2-3 years ago). So I highly doubt he is moving Liljegren... Especially when the greatest concern with the Leafs' defense right now is probably more to do with age than play style. Gio and Brodie are getting up there in age, as is Schenn if he is brought back, and all would be relied upon to handle important roles... Especially since Treliving has always had 3 good and reliable pairings on his team.
Timmins is probably the most likely to be moved, but that is also simply by virtue of being the most replaceable right now too; he was the #9 on our depth chart last year, and is almost certainly not going to be higher than #7 next year. He too can play a style that would fit well with what Treliving wants, and he looked good in the times he played with the Leafs, but his injury history may be a concern and hamper his ability to truly commit to that style as much as Treliving may want.
I do not think the defense is going to be as much of an "overhaul" as people think. An overhaul would be trading Brodie and replacing him with Dumba/Mayfield/Severson. Otherwise, I think it is more likely that he trades Timmins (probably for a mid-round pick), re-signs Schenn to be the #6/7 to rotate with Gio, and then finds a guy to play with Rielly, which could be Dumba/Mayfield/Severson (although word of warning about Mayfield for those who hate Holl: They are not that much different).
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I think his first move will be trading Murray with retention for a mid-round pick, or do something fancy with PIT and a team needing a cheap backup (i.e. Rangers):
RD Mark Friedman
3rd round pick 2023 (COL) - from NYR
5th round pick 2023 (PIT)
G Matt Murray (50% retained)
LW Nick Abruzzese
RD Mac Hollowell
G Casey DeSmith
Either that, or if he does make a move on defense, it could be Timmins for a mid-round pick to a team like ANA, or Hirvonen/Voit + 3rd for Borgen from SEA (Borgen would be a far better fit for us than anyone in UFA).