Big cat grabbing a deer's tail and part of throat (6)
I believe the answer is:
larynx
'part of throat' is the definition.
(I know that larynx is part of pharynx)
'big cat grabbing a deer's tail' is the wordplay.
'big cat' becomes 'lynx' (I've seen this before).
'grabbing' means one lot of letters goes inside another.
'tail' indicates one should take the final letters.
The final letter of 'deer' is 'r'.
'a'+'r'='ar'
'lynx' enclosing 'ar' is 'LARYNX'.
'and' is the link.
(Other definitions for larynx that I've seen before include "Human voice box" , "Site of the vocal cords" , "The formal voice-box" , "Where growls come from" , "part of pipe" .)