How do I change my bank card information so I can renew my subscription?

If you want to add a new payment card, you can do it here:

Settings > Apple ID > Media & Purchases > View Account > Manage Payments > Add Payment Method

Add your new card, after which you can delete your old one. When your new card is registered and your old card removed, subscriptions are paid from your new card.

Remember, you cannot remove your old card until the new one is added if you have an ongoing subscription.