From Longman Dictionary of Contemporary Englishloyalty cardˈloyalty card noun [countable] a card given by a shop, supermarket, etc to its regular customers allowing them to have advantages such as lower prices, money back on goods etc
Examples from the Corpus
loyalty card• Publishers' restrictions do not, for example, allow us to issue a Dillons customer loyalty card.• He had read her Sainsbury's loyalty card account.• I flashed my supermarket loyalty card and was in.From Longman Business Dictionaryloyalty cardˈloyalty cardCOMMERCE a card given by a shop, SUPERMARKET etc that gives regular customers lower prices, money back on goods etcThe loyalty card offers a 5% discount on the store’s own-brand goods. → card 