What is the relation between the Chaste and Iron Fist?

Question

The Hand is one of the prominent antagonists of the Marvel TV Universe, appearing in the first two seasons of Daredevil and Iron Fist. From the trailers, it also seems that defeating the Hand will be the reason of the creation of the Defenders team.

In these shows, the Hand has been opposed to two factions for centuries:

1. The Chaste, mostly represented by Stick, is an organisation whose ultimate goal is to destroy the Hand.
2. The Iron Fist, incarnated in present days by Danny Rand, is a warrior trained in the Himalayan monastery Kun'Lun to be the enemy of the Hand.

What is the relation between the two nemeses of the Hand?

I am mostly asking about the Marvel TV shows, but short of an answer from the shows, answers from the comics are welcome.

Answer 1

The Chaste, mostly represented by Stick, is an organisation whose ultimate goal is to destroy the Hand.

The Iron Fist, incarnated in present days by Danny Rand, is a warrior trained in the Himalayan monastery Kun'Lun to be the enemy of the Hand.

What is the relation between the two nemeses of the Hand?

I will answer according to the MCU Netflix series; I'm not sure what relationship (if any) there is in the comics. As you allude to, the answer to your question forms a part of the background to The Defenders series. Now that that series is out, we have a definitive answer.

Early in the series, Danny Rand and Colleen Wing realize they may have allies in the fight against the Hand, and attempt to track them down, but they arrive too late: the still-warm bodies are dead on the floor. Then, in episode 4, Royal Dragon, Stick shows up and explains the relationship between this organization, the Chaste, and the Immortal Iron Fist (Spoilers):

Danny Rand: He's one of them aren't you?
Luke Cage: The Hand?
DR: No. There's another organization.
Stick: We call ourselves the Chaste.
Jessica Jones: Ugh, these names are killing me.
S: And we're the only reason the Hand hasn't already won the war. We follow the elders of K'un Lun. And (bows to DR) the Immortal Iron Fist.
DR: The Chaste is my army?
S: Was. They're all dead now. Every one... except me.
DR: How come no one told me?
S: There are things I don't know.