It is a compound noun or noun phrase.
"vice president" is a noun phrase. President is a noun and vice is an adjective.
A phrase is never a part of speech, only a word.
The word they is a pronoun. The word are is a verb.
Prepositional phrase
"Ahem" is classified as an interjection, which is a type of word or phrase used to express a sudden or strong emotion or sentiment. It is commonly used to gain attention or to indicate a pause in speech.
The phrase "in addition" is a prepositional phrase in which "in" is the preposition and "addition" is its object. This phrase, as a phrase, is not a part of speech, although it may function as one, probably an adjective or adverb.
A prepositional phrase.
On the mountain top is a preposition phrase, not a part of speech.
That I am is a phrase, the individual words in the phrase are parts of speech. That -- demonstrative, determiner I -- pronoun am -- be verb
adverb phrase
verb
A prepositional phrase.