Sentences can be formed by phrases or clauses, in this case the italicized words are a phrase. A phrase is a grammatical unit composed by a set of words without subject and predicate whereas a clause is a grammatical unit formed by a set of words that includes a subject and a predicate.
The noun phrase “Wishing to be heard” is modifying the noun “speaker” since it is providing an explanation of why the subject is performing an action.