This owner has a pig (3)
I believe the answer is:
sow
'a pig' is the definition.
(I've seen this in another clue)
'this owner has' is the wordplay.
'has' indicates a hidden word.
'SOW' is hidden in the letters of 'this owner'.
(Other definitions for sow that I've seen before include "Female bear" , "farm animal" , "Scatter seed; pig" , "swine" , "Prepare farmland" .)