If you have more than 7 cards in your hand by the end of the turn, do you have to discard the excedent? For example, if you have 12 cards in your hand by the end of the turn, do you have to discard 5 of them?
There is no hand size limit in Pokemon, at all.
You can have a hand of 30 cards, or a hand of zero cards.
There are a few cards out there that can change that, but that would be a card effect and not a game rule.