I guess if you can buy tunes with it they should finish the job by turning on Apple Pay
Buying music and apps through the iTunes Store is no different than using your card through Amazon, eBay, or any other place online (in other words, Apple gets your card information and processes it accordingly).
For Apple Pay to work, the issuing bank or credit union has to support it, as they generate a unique number specific to your device. This is to add to the security, in that if you use Apple Pay, it uses that number that is different than the one printed on your card, but is generated by your credit union. They take care of matching the two behind the scenes when the transaction comes through. This is why many issuers can instantly update an Apple Pay card in the event that a physical one is lost or stolen and a new one gets mailed out - change the source account #, reassign the device #, point the two together.
For what it's worth, the generated number is the same type of number as your card, meaning that if you have a Mastercard, your device account number would also be a Mastercard (5xxx xxxx xxxx xxxx). This allows Apple Pay to work anywhere that has NFC, as the merchant just "sees" an Apple Pay payment as the card type you're using.
Most banks and credit unions support it, but there's a few smaller ones that don't for whatever reason. Discover was a notable one for credit cards, as they waited a year to support it, and still don't with their debit cards. Once that happens and you can add your card to the Wallet app, you should be fine.
Once the card is added, then you can load money on Apple Pay Cash, which, behind the scenes is a prepaid Discover debit card issued by GreenDot (they sell a lot of prepaid Visas/Mastercards at places like Walmart and Kroger). Unfortunately, the only way to fund and send money is from another card in Apple Pay.