As per usual, the answer is lawyers. There's a procedure where you can make a claim on a domain and take it over from the current owner... but I'm not sure that "I didn't renew it in time" is a good enough reason. You'll have better luck if this is a commercial related domain and you have some sort of legal claim (ie: trademark) over the name.

See section 4 of this article: https://www.godaddy.com/legal/agreements/domain-name-dispute...

You can also see this: https://www.godaddy.com/resources/skills/what-is-domain-squa...

I have no affiliation with GoDaddy - they just came up in some Google searches.