Is should've a verb or pronoun?

The contraction should've is a verb, a shortened form for the verbs 'should' and 'have'.
The contraction functions in a sentence as a verb or auxiliary verb.

Example:
We should have planned a little better.
We should've planned a little better.

A pronoun is a Word that takes the place of a noun in a sentence.

Example:

Jack and Jill were late. They should have planned a little better. (the pronoun 'they' takes the place of the nouns 'Jack and Jill' in the second sentence)