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Only six words place Y second and E third, and HYENA is the one anybody would recognise.
It is the only entry in ordinary use, and a puzzle reaching this pattern almost certainly wants it. Everything else here is archaic, legal or specialist.
Dyers colour cloth, eyers look at things and an oyer is a hearing in old English law. Three agent nouns from three unrelated verbs, all landing on the same closing letters.
Six letters open six words, one apiece. That is as clean a first box as this site offers, and it means the opening letter names the answer outright.
The trade off is that nothing else narrows. R takes the fourth box in three of the six and S closes four, but with a page this small those numbers tell you very little.
AYELP means in a state of yelping and TYEES are large Pacific salmon. Both are the kind of entry that exists in word lists and almost nowhere else.
So the practical advice is short. Try HYENA, and if the first letter comes back wrong, read the rest and pick.
A hearing or trial in old English law, surviving in the phrase oyer and terminer. It comes from the French for to hear.
Yes, the plural of eyer, one who eyes or watches. It is rare but valid and appears in standard word lists.
A large chinook salmon, in the Pacific northwest. The word comes from Chinook Jargon and also means chief.
Y followed by E needs a consonant in front and two letters behind. English builds very little that way, and what exists arrived from other languages or from older forms.