Purchases of subscriptions in the Clue app are managed by the App Store on iOS and the Google Play Store on Android. Charges to your account will be attributed to iTunes (iOS) or Google (Android) on your bank statement.
When you first subscribe to Clue Plus, you are immediately charged for the subscription you selected.
When your subscription runs out, it is automatically renewed. Both the App Store and the Google Play Store typically block the subscription cost between a few days and 2 weeks in advance (this process is called pre-authorization).