Is the semicolon used appropriately?

I’d like to ask if the semicolon is used properly/appropriately here?

He hadn't gotten to prove Daniel wrong; hadn't gotten to take his revenge for feeding him his first taste of defeat.

I’ve learned that semicolons should be used between two independent clauses so I’m not sure if it is used right here.

You are right in the lesson you learned. It is used between independent clauses. Your use is not quite right. "Hadn't gotten to take his revenge for feeding him his first taste of defeat." is not workable on its own. That is the test.

A substitute would be a comma. Others may disagree but the continuation of the thought would work with a comma. It sounds the same if delivered in a movie. That's my usual test.

"He hadn't gotten to prove Daniel wrong, hadn't gotten to take his revenge for feeding him his first taste of defeat."