Will My Mac Pro (late 2013) work with a new Apple Cinema Display

<< I'm trying to figure out if it will work at all with the proper adapter. >>

yes.

The Apple ThunderBolt-3 <-> ThunderBolt-2 adapter, US$50, supports genuine ThunderBolt displays (ONLY).

There are many far more affordable displays that you could consider, that do not require a US$50 adapter.

tvspotz Said:

"Will My Mac Pro (late 2013) work with a new Apple Cinema Display: Will My Mac Pro (late 2013) work with a new Apple Cinema Display [...]I have been using one old Apple Cinema Display from the same era and two other non-apple displays. Sadly the Apple display has breathed its last.[...]"

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View MY User Tip: It works for me on my 30" Apple Cinema Display: How To: Use a 15-Inch 2018 MBP with a 30-Inch Apple Cinema Display.

Try This Adapter: UPTap - USB-C to Mini DisplayPort Adapter 4K@60Hz - Silver - Amazon

Your 2013 Mac supports 5K resolution displays, but does not specify that is is at Billions of colors like most current Macs. (it may be 3 * 8 bit color. rather than todays 3 * 10 bit color)

The Apple ThunderBolt-3 <-> ThunderBolt-2 adapter, US$50, supports genuine ThunderBolt displays (ONLY).

we can't see your equipment, so precise terminology is all we have to share concepts.

Your cinema display is dead?

and you want to use a new Apple STUDIO display? or something else entirely?