To complete this quest you must fight to the top of Jintha'Alor and kill Vile Priestess Hexx. She will drop Hexx's Key which allows you to open Sharpbeak's cage. The cage is not in the cave behind Vile Priestess Hexx, it is through the north exit of the pit and is guarded by two mobs.
It is noteworthy to mention that a lot of mob clearing on the way up Jintha'Alor can be skipped by using a mount to run to the top.
Description
We must save Sharpbeak!
Fight your way to the top of Jintha'Alor in the heart of Vilebranch territory, gain the key to Sharpbeak's cage from the vile Priestess Hexx, and then find and save Sharpbeak!
Swiftwind and Keenclaw returned with their child moments ago, and are fussing over him like new parents. Seeing them together again is enough to give even this old dwarf mist in the eyes...
We cannot repay you enough for what you have done, <name>. The gryphons of Aerie peak, and their riders, will sing your name for a long, long time.