In chapter four of William Golding's Lord of the Flies, Jack has not had any success hunting pigs but has decided that it is because they can see him rather than smell him. His new tactic, then, is to paint his face. This is the "new face" to which you refer; Jack calls it "dazzle paint" and Golding refers to it as Jack's "mask."
[Jack] made one cheek and one eye-socket white, then he rubbed red over the other half of his face and slashed a black bar of charcoal across from right ear to left jaw.
This face paint serves as a mask, and the mask changes how Jack will act for the rest of the story. Golding writes:
the mask was a thing on its own, behind which Jack hid, liberated from shame and self-consciousness.
This lack of shame and conscience will allow Jack to do horrible things while hiding behind his painted face.