Big cat biting a rabbit's head and part of the throat (6)
I believe the answer is:
larynx
'part of the throat' is the definition.
'big cat biting a rabbit's head' is the wordplay.
'big cat' becomes 'lynx' (I've seen this before).
'biting' indicates putting letters inside (I've seen this in other clues).
'head' suggests taking the first letters.
The initial letter of 'rabbits' is 'r'.
'a'+'r'='ar'
'lynx' placed around 'ar' is 'LARYNX'.
'and' is the link.
(Other definitions for larynx that I've seen before include "Organ containing the vocal cords" , "The formal voice box" , "Cavity containing vocal chords" , "Upper part of the windpipe" , "Where growls come from" .)