Carnivore catching extremely valuable animal (6)
I believe the answer is:
beaver
'animal' is the definition.
(beaver is a kind of animal)
'carnivore catching extremely valuable' is the wordplay.
'carnivore' becomes 'bear' (bear is a kind of carnivore).
'catching' indicates putting letters inside.
'extremely' means to remove the middle letters (only the extremes of the word are used).
'valuable' with its centre taken out is 've'.
'bear' enclosing 've' is 'BEAVER'.
(Other definitions for beaver that I've seen before include "Dam-builder" , "Animal with soft fur, builds dams" , "Dam builder" , "Hard worker (could also be eager)" , "Semi-aquatic rodent" .)