Under the item description of the Staff of the Forgotten One in the ToA Hardcover, we see that a spirit inside the staff might try to possess the wielder:
The Forgotten One. The bodiless life force of a dead archmage empowers the staff and is imprisoned within it. The rune carved into the staff’s skull protects Acererak from this spirit’s vengeance. Each time a creature other than Acererak expends any of the staff’s charges, there is a 50 percent chance that the life force tries to possess the staff wielder. The wielder must succeed on a DC 20 Charisma saving throw or be possessed, becoming an NPC under the DM’s control. [...]
The Protection from Evil and Good spell can protect against some kinds of possession:
Until the spell ends, one willing creature you touch is protected against certain types of creatures: aberrations, celestials, elementals, fey, fiends, and undead. [...] The target also can’t be charmed, frightened, or possessed by them. [...]
If I were under the effect of Protection from Evil and Good, am I immune from getting possessed by the ghost of the staff?