'Her' is not a possessive pronoun here. It is an object pronoun. If you change the person, you can see this. I would like to hear you elaborate. I would like to hear him elaborate. Or change the verb. I would like to hear Taylor Swift sing. I would like to hear her sing.

I sent you a link to an online dictionary. And that is my violation.

There are a few verbs that can be followed by an infinitive without "to". The most common ones are "let", "make", "help", and all of the modal verbs. There are many others, though, and "hear" is one of them: I let her sing. ("her" is a direct object) I hear her sing. ("her" is a direct object) I hear her elaborate. ("her" is a direct object) I make her elaborate. ("her" is a direct object) I let her elaborate. ("her" is a direct object) She could elaborate. (no object) I listen to her elaborate. ("her" is an indirect object) It is a small list. You cannot do this with every verb. For example, you cannot say: "I like her sing" You would have to say "I like her to sing" or "I like it when she sings" or "I like her singing"