When a payer has requested to change the card details associated with an ongoing subscription you as an administrator can initiate an email to this person with a link to setup their new card details ensuring the payment will continue.
To begin the process login to the ClubZap admin portal and select the Membership link from the menu and select "Current Members".
Search for the name of the person you has requested the change.
In the payments section click on the button identified by 3 horizontal dots to reveal a sub menu.
Select the Cancel Subscription option which will result in no further payments taken form the existing card.
When the payment is in a cancelled state you can restart the payment by clicking the buttons similar to what's highlighted in this screenshot below.
Click on the Restart Subscription option to initiate an email to that persons email address. the email received will include a link to update their card details.