Khadgar is part of the quest chain that eventually leads to your acquiring , which you need to enter Karazhan.
Deliver Alturus's Report to Khadgar in Shattrath City in Terokkar Forest.
Alturus's report is unsettling. We thought it was bad when Karazhan sealed itself off to the outside world. We had agents inside; we never heard from any of them again. Now this... demonic emanation. We must investigate it.
The only people who can reopen Karazhan were presumed dead: Khadgar and Medivh.
While we hope that the latter is indeed gone, we recently learned that his apprentice, Khadgar, is alive and well in a place called Shattrath City. Find him and give him Alturus's report.
The Violet Eye? You don't say.
Show me this report you speak of.
Karazhan quest progression
This is part of the Karazhan Quest Progression quest chain.