The staff is recovered from Temple of Xrib Refugee Annex in Sightless Pit during Much Ado About Snow Elves. A few days after giving it to Calcelmo upon quest completion, a courier will deliver a note from Calcelmo. The staff can then be found on its display in the Hall of Lost Empires.
The staff will be brought along by Auryen during the quest 'Trial of Trinimac', and is required to open the front door to the Snow Elf Temple.
Temple of Xrib Refugee Annex in Sightless Pit
Location in Temple of Xrib Refugee Annex
Temple of Xrib Refugee Annex map