What part of speech is the word there'd?

Answer 1

The word "there'd" is an informal contraction for the pronoun "there" and the auxiliary verbs "would" or "had".
The contraction "there'd" functions as a subject and verb of a sentence or a clause.
The word "there" is a pronoun only when it introduces a sentence or a clause. The word "there" also functions as an interjection, an adverb, and a noun.

Examples:
There'd been music and food at the street fair. (subject and auxiliary verb)
They told me there'd be a sign on the door. (subject of the dependent clause and auxiliary verb)

Answer 2

The word "there'd" is a contraction of "there" and "would." It functions as a contraction for the subject and auxiliary verb "there" and "would." Therefore, it functions as a verb.