Pawn has hesitation getting a cat (4)
I believe the answer is:
puma
'cat' is the definition.
(puma is a kind of cat)
'pawn has hesitation getting a' is the wordplay.
'pawn' becomes 'p'.
'has' says to put letters next to each other.
'hesitation' becomes 'um' (sound made when hesitating).
'getting' says to put letters next to each other.
'p'+'um'+'a'='PUMA'
(Other definitions for puma that I've seen before include "Cougar" , "South American cat" , "Large wild American feline" , "Large Am. wild cat" , "Mountain lion" .)