The gilska remort quest begins in Glaviel. Gate to Lomal, and find the Curious Building. This is room is the entrance to the Great Spire. To enter the Great Spire, you need to say a password. There is an alabaster statue in Glaviel that includes the password in its object description.
Once you enter the Great Spire, Tlendin will give a you a series of tasks.
The first is to search Antrippa to find a crystallized orb of magma. You can find it on Gandor Isle. Each time you return to Glaviel, you will need to re-enter the the Great Spire through the Curious Building as before.
The second item is an ice crystal. Find this in Ebon Mining Outpost.
Next is the first fight, against a Death Spectre. The mob will not attack until you do, so you can leave to prepare. Once the fight begins, you cannot flee. The mob looks undead, but is immune to Destroy Undead.
After defeating the Death Spectre, you proceed to a series of mirrored rooms. Each room has a question to answer or an item to retrieve.
The first room was buggy for me, so I don't know the question.
The second mirrored room tells you to find the identity of Frellen and retrieve his crown. You can find this in Ice Barrow.
The third mirrored room tells you to retrieve an object from a necromancer in his grave. You can find this in Okeshir.
After the mirrored rooms is the second fight. You must discover the weakness of a beetle-like horror. The correct attack will kill this mob easily.
Next you search a library. Find all the pages and join them to create a book about gilska. Give this to the librarian.
After completing the quest, you are given a 'thought.' Use this object when you are ready to remort as a gilska.