loyalty card
US /ˈlɔɪ.əl.ti ˌkɑːrd/
UK /ˈlɔɪ.əl.ti ˌkɑːrd/

1.
a card issued by a retailer to a customer, used to record purchases and award points that can be exchanged for goods or discounts
:
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Do you have a loyalty card for this store?
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I used my loyalty card to get a discount on my groceries.