The word <em>with </em>in <em>Alexandra stomped out of the classroom with her entourage</em> is a preposition.
Explanation:
A <u>preposition</u> is a word used to link nouns, pronouns or phrases to other words in the sentence. A preposition does not only link words but also reveals what kind of relation there is between the elements of the sentence. For example, <em>with </em>is a preposition of possession.