loyalty card

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

:
Do you have a loyalty card for this store?
I used my loyalty card to get a discount on my groceries.