Once the card details leak, the real cardholder and issuer may learn about the data leak, i.e., be aware, or they may not, i.e., be unaware.
Data breach aware
If they learn about the leak, the primary option is to cancel the card and reprint it.
However, if details leak for too many cards, this may not be economically or logistically feasible because it would take too much time to reprint, ship, and activate all the new cards.
In that case, the issuing bank may temporarily or permanently take additional security measures to protect its cardholders.
Data breach unaware
If neither the issuer nor the cardholder learn about the leak, the cardholder will be vulnerable to credit card fraud.
Fraud may occur when the hacker who obtained the credit card details uses them to buy online services or products or, more likely, after fraudsters buy the credit card information on the black market and then pur- chase services or products online.
Finally, so-called mules  are sometimes used to pick up goods that are bought online.
- Wikipedia. Money mule; 2017.