If the triggered ability does trigger, that ability will check Ayara's Oathsworn again as it tries to resolve. If Ayara's Oathsworn has four or more +1/+1 counters on it at that time, the ability won't resolve. None of its effects will happen. You won't put a +1/+1 counter on Ayara's Oathsworn and you won't search for a card.

If Ayara's Oathsworn has four or more +1/+1 counters on it as it deals combat damage to a player, its ability won't trigger at all. None of its effects will happen. You won't put a +1/+1 counter on Ayara's Oathsworn and you won't search for a card.

If Ayara's Oathsworn isn't on the battlefield as its ability tries to resolve, you won't search for a card, even if Ayara's Oathsworn had three +1/+1 counters on it before if left the battlefield, because it won't be around to have the fourth +1/+1 counter put on it.