Standard users can have a maximum of 20 cards in their Pack at once. XL users with a subscription can have a maximum of 50 cards in their Pack at once. The dotted box at the top left of the screen shows you how many more cards you can add to your pack before it’s full (in this case, 8):
A card with a Pack Pet lock does NOT take up a Pack space, regardless of whether or not you're a standard or XL player. However, Pack Pet locks do take up a space until they're applied to a card!