From Destinypedia, the Destiny wiki
In combat, Envoys fight the same as most Taken Wizards except with a massive damage buff that allows them to kill nearly any target in one use of their Necromantic Gaze, however in return they summon Shadow Thrall far less frequently, only doing so if no target is in sight.
In Gambit, Envoys spawn alongside the Primeval and when killed, provide the team with a Primeval Slayer buff that enhances their damage output to the Primeval.
In Gambit Prime the Envoys served a different purpose, once the Primeval was summoned, three would spawn in a section of the map where ads would spawn during the mote collecting phase and guard a well of Light. Once killed the well of reclaimed Light would unlock and the team would then gain their Primeval slayer buff. This buff would last for 15 seconds after leaving the well. Each subsequent time the well is used would increase the Primeval slayer buff.