It is either a noun or a verb and can be used as an adjective.
the part of speech for city-state would be a noun
A dictionary will tell you the part of speech for each word. For example, the entry for "dictionary" will state noun.
Verbs show action or state of being.
The phrase "part of speech" does not contain any verbs.
Verbs denote the action or state of being in a sentence.
The word remoteness is a noun. It is a state of being remote.
The part of speech for "officially" is an adverb. It modifies verbs, adjectives, or other adverbs to provide more information about the action or state conveyed in a sentence.
The word peace is a noun. Peace is a state of harmony or tranquility.
Solitude is a noun. It refers to the state of being alone or isolated.
State can be a noun or a verb. In this sentence it is a verb: State your name, please. In this sentence it is a noun: What state do you live in?
Turmoil is a noun. It refers to a state of great disturbance, confusion, or uncertainty.
The word verb is a noun, a word that expresses an action, state, or occurrence.