Sleep Cycle has an optional annual Premium subscription.
Once you're a subscriber, you can manage your subscription from iTunes or on your iOS unit after purchasing it, and you'll also be able to cancel the auto-renewing subscription from there. For detailed instructions on how to do this on all platforms and devices, go here.
Please note, deleting the app does NOT cancel the subscription. You can, however, cancel a subscription even after you've deleted the app.
The subscription will auto-renew 24 hours before the subscription period ends, with the same subscription you already purchased, at the same price. Please ensure you cancel before this time to avoid being charged.