The meaning of this sentence is ambiguous because of the present simple.
It could mean, "You never do any homework, and when you start doing homework, you'll have permission to listen to some music." Or it could mean, "After you have finished your homework, you'll have permission to listen to some music."
Either way, it's a future condition about a future result, so it's closest to first conditional. It doesn't represent eternal truths, so it's not zero-conditional.
It's also used with present perfect. This sentence with present perfect would only have the second meaning above.
And contrary to answers from other people, the sentence is correct, and pretty natural, at least in North America.
This structure in this context indicates denial of permission to do something until some other condition is met. Parents and teachers use it all the time. It's almost only said to children.