From Destinypedia, the Destiny wiki
Wealthy Knights are a unique type of Major Hive Knights, as well as a powerful High-Value Targets that are found in the Gambit activity, and Gambit Prime before it was removed. They can be told apart from their regular counterparts with the white glow around them.
Wealthy Knights will appear in Gambit matches that take place on the maps Deep Six, Emerald Coast, and New Arcadia – specifically when your up against the Hive. They will only appear once per match, so you and your Fireteam will have one shot at eliminating them before they are gone.
Not long into the match, the Drifter will announce that a High-Value Target is on the field. Once they have arrived, they will begin to quickly make their way to the opposite side of the map. Players will have a limited time to the kill them before they reach their destination. If this happens, the Drifter will say that they target is preparing to depart, and you will only have a few seconds left to kill them before they despawn. Although the target has a large amount of health, they will bleed Motes of Dark as they take damage, and if you are successful in killing them, they will drop a substantial amount of Motes.
List of appearances