The 4WD in the jeep isn't engaging at all in 4H, but 4L works just fine. 2WD is also working just fine and I have no trouble shifting it into 4L and back to 2WD. It doesn't "thud" or drop into 4H and I am positive that it's not engaging/working, the handle moves very freely between 2H and 4H and doesn't catch at all.

I am wondering if anyone has an experience with this or thoughts on if it's likely to be a linkage issue or transfer case issue given that 4L works but 4H doesn't.

It's a 2000 Cherokee Sport with a command trac, N231 transfer case.
I haven't used the 4WD in a couple years. I just moved up north and we got out first snow/ice when I noticed the problem.
I've always been careful to only use the 4H on slick surfaces and know how to properly shift it into 4L.
May be entirely unrelated, but it's always (even when 4Hi worked) had an occasional rattle/hum sound which is easily corrected by pushing the Tcase shifter handle a little further forward to 2H.

What makes you think it isn't engaged? Does the light come on?

The part time light does come on. I drove it around and it doesn't feel like it engages, had some friends drive it around who agreed and couldn't see the wheels all spin when it was slipping and took it to the shop where they confirmed the 4H isn't working.

Does the front axle have a vacuum disconnect?

I don’t think so. It’s a 2000 so I’m pretty sure it’s got a solid front axle

I’m having the same exact problem, My hunch is that my shift fork pads are burnt up but curious what others have to say about this

Check to see if the gate on the shifter is preventing it from going into 4HI properly. Otherwise, it's the shifter pads...

Are you shifting to 4H while moving like you're supposed to?

So I am new here and both work on my jeep, but to be clear (don't have the book)...

4H: in drive moving slowly put it in 4wd
4L: In neutral stopped, put in 4wd

I'll check out the shifter pads and the gate and report back! Thanks for the input

Yep- thats what I've always done.
4H while moving, shift with foot off accelerator, drop into 4H, give it gas.
4L while barely moving (like 2 mph), put in neutral, drop into 4L, back to Drive, and give it up some gas.

2 high to 4 high and back at any legal speed. I've done it at 80 MPH.

my 4H works in reverse but not forward. 🤔

Your shift fork needs new teflon tabs on it