Once you have received the new credit card information from your Donor you can go into their record and enter the card in on the Payment Options tab. Once the new card has been entered navigate to the Gifts tab and launch the Pledge record you'd like to switch the card on. 

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.