An adverb clause is a type of a dependent clause that modifies or to add more detail to an adjective, a verb or another adverb. This type of clauses often answers questions such as "Why?", "How?", "When?", "Where?" and "In what circumstances?".
In the provided sentence, "better than he did last year" is the adverb clause for the following reasons:
It is a dependent clause: It can not stand on its own and express a complete thought.
It modifies the verb "play" since it answers the question "How does Gary play the trombone?"
I would choose D. It isn't A because there isn't a clear comparison in the passage. It isn't B because there is no contradiction. C simply doesn't make sense. If you had a strong feel why would you make it seem insignificant? So that is why I picked D.