There isn't a self-service "change card" button yet. You have two options:
Cancel the subscription (one click on /applicant/subscription) and start a new one with the new card the next time you apply. The new subscription is at the price offered then.
Or send a change request (/help/change-request, "Something else") from the e-mail on your account, and a person will help — we never ask you to send card numbers by e-mail.
If a renewal fails because a card expired, the subscription shows "Past due". You can cancel it at any time, and nothing more will be charged.
Something not right with a charge?
Send a change request: billing mistakes our records prove are refunded automatically, and a person answers the rest within two business days.