Rielle's first ability applies only while it's on the battlefield.

If you discard a card as a cost to cast a spell or activate an ability, Rielle's triggered ability resolves before that spell or ability but after you've chosen targets for it. If you discard a card while a spell or ability is resolving, that spell or ability finishes resolving before Rielle's triggered ability does.'

If the first time you discard cards during your turn is due to having too many cards in hand during your cleanup step, you'll draw that many cards. Players will receive priority during the cleanup step in this case, and a new cleanup step will happen after that one, during which you may have to discard cards again.