Dealing with 4 attack as Priest

Aside from your damage spells, remember that you can sometimes buff or debuff the enemy minions from 4 attack to 3 or 5 attack.

For example: If somebody uses a Chillwind Yeti and you apply your Dark Iron Dwarf effect on his Yeti, it will make his Yeti 6 attack, which will allow you to use Shadow Word Death

How can a Priest deal with 4-attack minions? The same way everyone else does.

Priests are unique in that they have special removal options for creatures of power 3 or less, and power 5 or greater, but that doesn't mean you don't have the same sorts of options others do.

Mainly, direct damage, offensive creatures, and defensive creatures.

Priest have access to excellent direct damage, including Holy Smite, Holy Nova, and Holy Fire. Shadowform is an option too.

You can also use all sorts of creatures for enemy minion removal. Charge minions are great for this, as are minions with high toughness and/or taunt, as you can continually heal and buff them with your hero power, Divine Spirit, and Power Word: Shield.