The staff is recovered from the Alftand Refugee Annex in Alftand 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 placed in the Hall of Lost Empires.
The staff will be brought along by Auryen during the Trial of Trinimac and is required to open the left door in the Snow Elf Temple.
Irkngthand Refugee Annex
Location in Alftand Refugee Annex
Alftand Refugee Annex map