Because of the 3DS regulation, it's not possible to change the card information while you have an active subscription. It is very important that you do the process one day before the billing date (if next billing date is for example on 23.3., you do the process on 22.3.) so you don't pay for the same period twice.
First, you need to cancel the subscription here
Click on the small trash icons to delete existing data and then insert the new card information here
Once you have inserted all necessary information, you need to go back to this page and activate the subscription.
NOTE: Be aware that subscription cancellation is immediately! Just click once and then wait for the system to respond. If everything is alright, then you'll get a green notification. If there was some kind of error, you'll get a red notification with written explanation.