As long as the pricing of your Subscription is not set to lifetime, the subscription will issue a renewal. Whether or not payment is automatically taken would depend on your payment method and the settings you have configured for it.
For example, PayPal would need to use what they call Billing Agreement/Subscriptions. You have the option for to allow the user to opt into automatic payments, force automatic payments, or not allow automatic payments.
For Stripe, the user must agree to leave their credit card details on file (with Stripe) in order for automatic payments to work.
If they do not opt in to automatic payments or you do not allow them, the user would need to manually pay the issued invoice.