Longman Dictionary of Contemporary English
loyalty card
noun
EXAMPLES FROM CORPUS
▪ He had read her Sainsbury's loyalty card account.
▪ I flashed my supermarket loyalty card and was in.
▪ Publishers' restrictions do not, for example, allow us to issue a Dillons customer loyalty card.
Wiktionary
loyalty card
n. A plastic card used in a company's loyalty program, which rewards customers who make regular purchases.