Changing from paid through app store to paid app outside of app store

Hi everyone, we have a subscription-based app that users purchase through the app store. For various reasons, we're considering having new subscribers purchase app through our website only and not through app store. (like Kindle app). I'm wondering what happens to the users who already purchased through the app store. Will they continue to have their subscriptions automatically renewed through app store, even though the subscriptions will have to be removed for future users? Or will current users have to cancel subscription through app store and resubscribe through website?

All feedback is appreciated. :)
Thank you!