This is really unfortunate, but to even start your journey to getting The Chaperone you are going to just flat out have to get lucky. It appears that you have a chance to receive the quest you need to start this journey is a random reward from completing and participating events. There's been reports of getting it after entering The Dreaming City, playing Crucible, dismantling armor/weapons, or completing/entering a Strike. Suerte ✌️