Word before peeve or project (3)
I believe the answer is:
pet
'word before peeve or project' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for pet that I've seen before include "Favourite - maybe teacher's" , "Cherished favourite" , "Particular favourite" , "Cat or dog" , "Favourite; fit of the sulks" .)