The previous owner of the dog was a wizard (4,6)
I believe the answer is:
past master
'a wizard' is the definition.
(I've seen this before)
'the previous owner of the dog' is the wordplay.
'the previous' becomes 'past' (I've seen this in another clue).
'owner of the dog' becomes 'master' (I am not sure about this - if you are sure you should believe this answer much more).
'past'+'master'='PAST-MASTER'
'was' acts as a link.
Can you help me to learn more?
(Other definitions for past master that I've seen before include "Expert - former office holder" , "Thomas Arnold was" , "Someone with a long and thorough experience in a given activity" , "wizard" , "Adept fellow" .)