Self-importance central to Gregory (3)
I believe the answer is:
ego
'self-importance' is the definition.
(I know that self-importance can be written as ego)
'central to gregory' is the wordplay.
'central' says to take the centre.
The central letters of 'gregory' are 'EGO'.
(Other definitions for ego that I've seen before include "(Person's) sense of self-esteem" , "In Virgil I" , "Conscious mind" , "One's image of oneself" , "Personal pride" .)