The Green Grace is a high priestess of her order, the Graces. There appears to be only one Green Grace per Temple of the Graces. The Green Grace of Meereen is Galazza Galare. There is another Green Grace in Astapor and presumably one more in Yunkai.
A Dance with Dragons
The Green Grace of Meereen, Galazza Galare, acts as an advisor to Queen Daenerys Targaryen while she is reigning in Meereen. Two of Daenerys's favorite cupbearers and hostages are Qezza and Grazhar, cousins to the Green Grace.
The last Green Grace of Astapor remains unnamed. During the Siege of Astapor, this Green Grace had a vision that Cleon, the Butcher King, could save the city from the besieging forces of Yunkai, despite the fact that the man was already dead and buried. The corpse of Cleon was fitted back into his armor and strapped onto the back of a starving horse, which led the remnants of his new Unsullied on a failed sortie. They encountered a legion from New Ghis, however, and were all killed. For her failed prophecy, the Green Grace of Astapor was impaled upon a stake in the Plaza of Punishment and left there until she died. Quentyn Martell, one of the besiegers, recalls the priestess in her torn robes, impaled upon a stake and attended by a cloud of glistening green flies.