At the end of the gift period, it depends on whether you already had an active monthly subscription.
If you did have an active monthly subscription, that was paused for the length of the gift, and will automatically restart on your next monthly due date. For example, if your monthly subscription gets billed on the 6th of each month, and you activated your gift membership on Dec 1st 2019, you had 5 days remaining of the monthly subscription before your annual gift kicked in. You'll therefore next be billed on Dec 6th 2020.
If you didn't have an active monthly subscription then the account will automatically revert to a free membership following the gift's expiry. You can renew the membership at any time before or after the expiry, to continue the paid member benefits.