Debit card
How can I set up my debit card so only I can use it
iPhone XR, iOS 12
Where are you trying to add the card? Are you a Family organizer? If the App Store/iTunes, if you go the Settings/iTunes & App Store, and sign out of your Apple ID, unless someone else knows your Apple ID, and can sign back in, no one will be able to use the card.
If that isn't what you mean, more information would help.