We meet Greef Karga as a member of the bounty hunting guild who hands out the bounties to the interested hunters.
It seems that the original plan was for Karge to get shot by Mando while he made his escape.
That’s actually exactly what happens in Chapter 3 of the series, though in the version we saw, we learn that Karga survived being shot.
He gives Mando the bounty for The Child in the first episode, and in the third episode, after Mando makes the decision to rescue the little green alien, Karga is one of the hunters trying to catch the Mandalorian and get the child back.