I've previously speculated that the Faceless Men are probably working for the White Walkers, even if they don't directly know it.
They worship the God of Death, or the very concept of death. Melisandre has made it very clear in the books (not the show, unfortunately), that the Lord of Light has an opposite, a Lord of Darkness who empowers the White Walkers and their undead army. Even though Wights are "resurrected", they are very much dead, not like those resurrected through the Lord of Light's powers.
Melisandre also makes it clear when speaking to Davos that the Lord of Darkness has human agents who pursue his will unseen in the normal world. Who are these people? Have none of them been introduced yet? I find that highly unlikely. Who seems interested in engendering chaos in the world?
Aside from the obvious choices of Euron and Littlefinger, you have the mysterious group of the Faceless Men.
Why are they in Oldtown sneaking around? I think they have some vested interest in sabotaging Dany's return to Westeros. If you recall, their religion began because of the subjugation of people by the Valyrians. They are now a death cult who sacrifice their individuality to offer the gift of death to those who want it or are willing to trade their humanity for it. Why else would they be spying on Marwyn, who wants to help Dany?