Dad, with hesitation, gets cat (4)
I believe the answer is:
puma
'cat' is the definition.
(puma is a kind of cat)
'dad with hesitation' is the wordplay.
'dad' becomes 'pa' ('pa' can be a synonym of 'dad').
'with' is an insertion indicator.
'hesitation' becomes 'um'.
'pa' placed around 'um' is 'PUMA'.
'gets' is the link.
(Other definitions for puma that I've seen before include "Panther" , "Large American feline resembling a lion" , "American wildcat" , "South American cat" , "South American carnivore" .)