Axem is found in the Museum, in the North West area of the Royal city.
He gives 3 quests requiring items of varying rarity, these items can be found as loot on almost any creature in Ter Mur, the Abyss or Underworld.
I find it best to collect the items as I come across them during hunting rather than set out to hunt for them specifically. This is especially true of the item for the third quest.
A Broken Vase
This quest requires 10 Ancient Pottery Fragments, the reward is a Meager Musem Bag, typical contents as shown (3,000gp approx), and 5 loyalty points.
Putting the Pieces Together
This quest requires 5 Tattered Remnants of an Ancient Scroll, the reward is a ‘Dusty Museum Bag’, typical contents shown below (6,000gp approx), and 15 loyalty points.
Ye Olde Gargish
This quest requires an Untranslated Ancient Tome, a dark colored book of the same size and type as the books in the reward bags pictured. It is rumored to drop frequently from Navrey Night Eyes though it has a chance of dropping from any creature whose loot table includes pottery fragments or scroll remnants. The reward is a ‘Bulging Museum Bag’ (10,000gp approx) and 50 loyalty points