The number of cards in your hand is checked at the beginning of your upkeep before you have the opportunity to cast spells and activate abilities. If you have seven or more cards in your hand at that time, Damia’s last ability won’t trigger.

After the ability has triggered but before it resolves, you have the opportunity to cast spells and activate abilities.

When Damia’s triggered ability tries to resolve, if you have seven or more cards in your hand, it will have no effect. If you have fewer than seven cards in your hand, you’ll determine the difference and draw that many cards.

Effects can modify the number of cards you’ll draw. For example, if you have four cards in your hand and control Thought Reflection (“If you would draw a card, draw two cards instead.”), you’ll draw six cards.