The only way to add a new card to your account is to process a new purchase or renewal, it is no longer possible to add a card through your contacts and billing section.
If you need to make a renewal you would need to first add the product to your basket from the renew services section of your Heart account.
Once you've added it to your basket you would need to go to the checkout, and once you are in the checkout process you should see the option to add a new card. Enter your new card details and proceed through the payment and this should process your renewal.
Once you've added the card through the steps outlined above, this should save the card to your account.
If you need to remove old cards from your account you can still do so via the Contacts and Billing section > Billing details.
If you are purchasing a new product you would also need to add a card via the same method as outlined above.