Quiet’s story goes through a number of sharp turns, from the way she breathes through her skin, to her defecting to the Diamond Dogs, to her ultimate separation from Big Boss entirely, eliminating her as a Buddy for missions, with, originally, no way of getting her back.
This newest patch requires the player to start and complete the mission “Cloaked in Silence” seven times. Upon the seventh attempt, the mission’s title will change to “[Reunion] Cloaked in Silence”. The completion of this will allow Quiet to be once again available as a Buddy for future missions.
The mission involves eliminating or simply neutralizing Quiet. The walk-through linked above does add that while lethal weapons can be used against her (the sniper rifle being the most effective), that she will survive the fight either way and become an ally later on. Though this is in regards to first acquiring Quiet as opposed to recovering after losing her.
Metal Gear Solid V: The Phantom Pain is currently available for PlayStation 3, PlayStation 4, Xbox 360, Xbox One and PC.