This owner has a pig (3)
I believe the answer is:
sow
'a pig' is the definition.
(I've seen this before)
'this owner has' is the wordplay.
'has' indicates the answer is hidden within the clue.
'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" .)