I forgot to mention that the screw that secures the zinc should be ordered and replaced too as it usually deteriorates and will sieze. But if you're correct that the zinc is gone then that's already happened.
Hopefully you get lucky and find someone took it out and forgot to put it back...you know..."hey, here's an EXTRA part I don't need"!
If you have to drill that screw out, I like to use a "gouger" in my Dremel called RESCUE BIT. Kind of like "voodoo magic" for removing broken off screws and bolts.They are expensive bits but will last several jobs IF you follow the company's instructions. If you don't use them as instructed you will damage and ruin the bit straight away.
Good luck with your projects!