A case refers to a "binding" or authoritative decision made by the court. Binding is a verb, noun or an adjective?
It’s very much an adjective in a binding decision.
Adjective: a binding decision
In a binding decision, the word binding is an adjective, not something else.
It was originally the -ing inflection of the verb to bind, but is no longer a verb. It isn’t a verb because it cannot take object arguments here. You can’t have “a binding their wrists together decision”. (This was not a very good argument; see below for better ones.)
The OED calls binding in this sense a participial adjective to signal its origin.
In a comment, BillJ offered much better syntactic tests than my lame one proving binding is an adjective here:
"Binding" is not a VP here, but a participial adjective. It has syntactic properties of indisputable adjectives and hence must belong in that class. For example, it can be modified by very, which can't modify verbs; it can occur as complement to complex-intransitive verbs like seem (It seemed quite binding), or complex-transitive verbs like find (I found it quite binding).
If you want just one short reason to remember, then because it can be a very binding decision, it can be neither a verb nor a noun, only an adjective.
Noun: a binding manual
For an example where binding is a noun, consider that if you didn’t know how to bind books, so you went off searching for a binding manual. That’s not a manual which “is” binding the way the decision “is” binding, but rather it’s a manual that’s “about” or “for” binding. That means binding is a noun there. Notice you can’t modify it with very and say *a very binding manual. You can’t have a manual explaining “very” binding.
Verb: binding your wrists
For binding to be a verb, we can go back to the example of binding your wrists. There it’s definitely a verb because it has a direct object.