I have a solution for you to add a hitch, but unfortunately there are only Class I hitches made for the 2021 Corolla hatcback. With that said, the Curt # C11567 is well made and will provide you with a hitch that has a durable powder coating that can stand up to nicks and scratches fairly well, so it's going to do a good job of resisting rust/corrosion.
I've linked a review and installation video of this hitch for you to check out, as well. view full answer...
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