The Wise Old Man wears a unique outfit that cannot be obtained by any means in-game; they exist only for that NPC. Unless Jagex adds the outfit to Solomon’s General Store or the Loyalty Shop (or any other redeemable means in-game as a reward for completing a quest related to the WOM), his outfit will remain unique.

It may be possible the Wise Old Man’s garb could appear as an outfit set in Solomon’s General Store, given that there are sets for Ariane’s outfit and Ozan’s outfit, however the chances are fairly slim.