Similar to anaphora, referring to a word that refers to itself, is there a phrase for a pair consisting of a word describing a person and an adjective that describes it?
EDIT: To clarify: In the sentence, "Harry is a gifted singer", I'm referring to the pair (Harry, gifted) specifically where Harry is the person, and gifted is the adjective, where gifted describes Harry
The main point of Eleshar's answer and BillJ's comment seems to be that there is no explicit terminology because gifted is a modifier of the predicate singer rather than in direct interaction with Harry.
This is true syntactically:
1
As expressed by the arrow labelled "amod" going from the NN singer to the JJ "gifted", gifted is an adjectival modifier of the noun phrase singer, which is itself the subject complement of the verb to be which acts as a copula between Harry and the noun phrase ("nsubj" = Harry is the "nominal subject" of the NN singer).
The syntactic status of gifted is defined with respect to the predicate singer which the adjective modifies, but it stands in no direct relation with Harry, only indirectly via the "nsub" relation from singer to Harry.
This is why it was said by others that there is no term for this kind of indirect relationship.
x is a ADJ NOUN
as
ADJ(x) ∧ NOUN(x)
which basically means that the predicate ADJ applies to x and the predicate NOUN applies to x.
Under this account, the adjective and the noun are treated equivalently as predications over an individual; the adjective is not a modification of singer, but the nominal complex gifted singer is viewed as a conjunction (∧) of two properties that apply to a certain individual x.
This reasoning might be easier to understand with a sentence like
Harry is a purple zebra
PURPLE(harry) ∧ ZEBRA(harry)
where it is clear that Harry being purple is just another property that applies directly to Harry, and Harry's being a zebra is another property.2
Under this account, the adjective gifted is not a modifier of the subject complement singer, but a direct predication of Harry.
You could thus say that (Harry, gifted) is a predication relation: Harry stands in relation with gifted by gifted being a predicate over (= a property that applies to) Harry. To make it more precise, you can say that it is an adjectival predication.
1 Image obtained from the Stanford CoreNLP online dependency parser
2 I am fully aware that this approach doesn't work for arbitrary sentences of this form; clearly, in a sentence like Harry is an alleged murderer, it doesn't make sense to say that alleged is a predicate that applies to Harry. In such a context, the adjective does act more like a modification of the property of being a murderer; in this respect, it behaves a bit like an adverb modifying the "to be" relation ("Harry is allegedly a murdrerer", i.e. the "to be" relation is modified in the sense that it is not necessarily true). However, in the example given, I think it's okay to say that being talented is a property that applies to Harry himself, so I'll stick to the simplistic conjunction approach.
In your example Harry is a gifted singer, the word gifted is just a general attribute/modifier in an adjective phrase and there is no grammatical relation between gifted and Harry because gifted modifies solely the noun singer and is totally governed by it. I suspect that would be pretty much a universal case even in languages that employ verbs in place of adjectives and conjugate them (e.g. in I am a gifted singer, the verb to be gifted would be in 3SG and agree with singer).
What I suspect you are aiming at is the term complement, particularly subject complement. This is typically a simple adjective predicate like Harry is gifted but may be more interesting like Harry got sick. The general idea behind it is that it is connected to the noun typically in subject, but not as a general modifier in adjective phrase but through a transitive verb.
The subject complement is, of course, not restricted just to adjectives, e.g. in your example, the entire DP a gifted singer is basically a subject complement in itself.
Then there are also object complements, typically in some quasi-causative constructions like This makes me sick. Here there is a similar relationship between the adjective sick and the object me, established through the ditransitive verb make.
