I was starting to wonder if I was doing something wrong while I was on this quest, but as it turns out the item just has a low drop rate.
Here are the quests you need to complete A King’s Defense (provided by user MBR08):
1. Complete Quest: Chaturanga Opening in Malevolence, Edengrove.
2. Complete Quest: White’s First Move in Scorpius, Mourningdale.
3. Complete Quest: En Passant in Eridanus, Restless Shore.
4. Complete Quest: Shahnameh’s Story in Periville, Weaver’s Fen.
5. Complete Quest: The Touch-Move Rule in Stone Skull Fort.
6. Complete Quest: The Pawn’s Promotion in Caminus, Shattered Mountain.
7. Complete Quest: Castling The King in Mangled Pox Gate and Nihili Visage, Great Cleave.
8. Complete Quest: Rook’s Checkmate in Myrkgard, Shattered Mountain.
Prerequisite to A king’s Defense (and the other legendary items questlines):
Also, you must have 20 weapon skill in your weapon of choice to be able to start the weapon’s related questline.