Whenever another creature enters the battlefield under your control, you may discard a card. If you do, put a +1/+1 counter on that creature, it gains haste until end of turn, and it becomes a Vampire in addition to its other types.
You decide whether to discard a card as the triggered ability of Olivia, Mobilized for War resolves. If you do, the rest of the ability’s effects happen before any player may take actions.
If the entering creature leaves the battlefield before the triggered ability of Olivia, Mobilized for War resolves, you may still discard a card. The rest of the ability has no effect.
If you discard a card, the creature only gains haste until end of turn, but the +1/+1 counter and Vampire subtype remain indefinitely.