Speak with Alchemist Arbington at Chillwind Point, Western Plaguelands.
On the island of Caer Darrow lies Scholomance - a wretched center of Scourge necromancy and evil. Our enemy dwells within, conducting unspeakable acts of depravity on unwitting victims... at least, we surmise as much. A door bars the way, and try as we might no entry is to be had without a proper key.
Alchemist Arbington is well versed on Scholomance, and has an idea how to obtain a key. You have proved your worth to me, and now I entrust this task to you. Speak with him on this matter.