The expiration date listed on your Annovera ring works a little differently than other birth control. The expiration date reflects the last point when the ring can begin to be used for the 1 year cycle. Meaning, the ring would be effective for a period of 364 days so long that it is inserted before the expiration date listed. For example if the expiration is May 31, 2021 that is the last day the ring can be inserted and used for the year.
reference: https://www.pharmacytimes.com/publications/issue/2020/june2020/important-education-for-patients-regarding-a-long-lasting-reversible-contraceptive