Breed of pet rat eating pork pie wife brought around (10)
I believe the answer is:
rottweiler
'breed of pet' is the definition.
(breed of dog)
'rat eating pork pie wife brought around' is the wordplay.
'rat' becomes 'rotter' (synonyms).
'eating' is an insertion indicator.
'pork pie' becomes 'lie' ('pork pie' is Cockney rhyming slang for a lie).
'wife' becomes 'w'.
'brought around' shows that the letters should be reversed in order.
'lie'+'w'='liew'
'liew' back-to-front is 'weil'.
'rotter' going around 'weil' is 'ROTTWEILER'.
(Other definitions for rottweiler that I've seen before include "Fierce dog" , "Large black/tan dog" , "Powerful German dog" , "Dog used as guard - let wire rot (anag)" , "Large and powerful dog, originally from Germany" .)