Old lady's pet dog (7)
I believe the answer is:
mastiff
'dog' is the definition.
(breed of dog)
'old lady's pet' is the wordplay.
'old lady's' becomes 'ma's' (both can mean mother).
'pet' becomes 'tiff' (I've seen this in other clues).
'mas'+'tiff'='MASTIFF'
(Other definitions for mastiff that I've seen before include "Large short-haired dog breed" , "Powerful, smooth-coated dog used for security work" , "Powerful dog breed" , "Large, powerful, short-haired dog" , "Hound" .)