Incredibly cute rare animal (8)
I believe the answer is:
creature
'animal' is the definition.
(I know that animal can be written as creature)
'incredibly cute rare' is the wordplay.
'incredibly' indicates an anagram.
'cute'+'rare'='cuterare'
'cuterare' is an anagram of 'CREATURE'.
(Other definitions for creature that I've seen before include "Animal or person" , "Bird, beast, insect etc" , "Brute" , "These comforts make life easy" , "Bird, beast or fish" .)