Father has hesitation getting a cat (4)
![Ross](/clue/static/ross-mug.min.png)
I believe the answer is:
puma
'a cat' is the definition.
(puma is a kind of cat)
'father has hesitation' is the wordplay.
'father' becomes 'pa' (pa is a kind of father**).
'has' is an insertion indicator.
'hesitation' becomes 'um'.
'pa' enclosing 'um' is 'PUMA'.
'getting' is the link.
(Other definitions for puma that I've seen before include "American wild cat" , "Cougar" , "American wildcat" , "South American cat" , "Large American feline resembling a lion" .)