All-consuming (9)
'all-consuming' is the definition.
(I've seen this before)
This is the entire clue.
(Other definitions for obsessive that I've seen before include "Showing continual preoccupation" , "Compulsive, all-consuming" , "Continually preoccupied" , "Under a strong compulsion" , "Compulsive, fixated" .)
(Other definitions for voracious that I've seen before include "Having great appetite" , "Eating food in large quantities" , "Excessively greedy" , "Ravening" , "Eager" .)
(Other definitions for omnivorous that I've seen before include "Eating everything" , "All-devouring" .)