Hawk swallowing head of rare fish (5)
I believe the answer is:
trout
'fish' is the definition.
(trout is a kind of fish)
'hawk swallowing head of rare' is the wordplay.
'hawk' becomes 'tout' (I've seen this before).
'swallowing' is an insertion indicator.
'head of' says to take the initial letters.
The initial letter of 'rare' is 'r'.
'tout' placed around 'r' is 'TROUT'.
(Other definitions for trout that I've seen before include "Freshwater game fish" , "Game fish related to salmon" , "air" , "one may be hooked" , "It rises to fly" .)