Once you have received the new credit card information from your constituent you can go into their record and enter the new card or edit and existing one in the Payment Options tab. A constituent may also update their payment information via their portal.
If you were only updating the card, the new information will be automatically reflected in the pledge. If you added a new card, you will need to update the pledge. Navigate to the constituent's Pledges Tab. Open the pledge to be modified by clicking on the pledge amount.
With the pledge open, find the Payment Method drop-down, on the left just above the Payment Schedule. Select the drop-down and switch the selected value from the old card to the new and save the record. Once the old card is no longer linked to any donations it can be deleted on the Payment Options tab. Deleting the old card will stop any Credit Card Expiration notification emails.