Psyche division (3)
I believe the answer is:
ego
'psyche division' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for ego that I've seen before include "Self-esteem, sense of self" , "Conceit - the Latin "I"" , "Inflated pride" , "In Virgil I" , "Person's sense of self" .)