Hi there,
Sure - we can do that. First, can you confirm that your Department entries into your field are displayed exactly the same as your Departments in AAD? We will be checking against AAD to identify the accuracy, presumably!
I've created a list for myself to demo on:

My department in AAD is "Consulting", so our goal is to get an update on the first entry, and a skip on the second. I am also making the assumption that you will only have one entry per person - if there are several entries per person, then, there might be a more efficient way to do this 🙂
⭐Step 1 - Create a scheduled recurring flow for once a day (or weekly or whatever suits you.)
⭐Step 2 - Add a "Get Items" action and point it at your list.
⭐Step 3 - Add a condition: On the left hand "Choose a value" side, add "PersonField Department" (in my case, it's called AssignedTo Department". On the right side, click and select your "Department" field. ⚠️ Your condition will now be within an "Apply to each" and that's exactly what we want!
⭐Step 4 - On the "Yes" side, we do nothing - the departments are right! I'm adding a Compose in mine as a note, because ... well, I like to. On the "No" side, we are just going to update the current item with the "Assigned To Department" in the "Department" field.
All in all, it looks like this:

After running it, my updated list looks like this:

And the one that ran on the item with "Consulting" already as the Department (correctly), shows this in the run:

Cheers,
Rhia