Favourite part of Morpeth (3)
I believe the answer is:
pet
'favourite' is the definition.
(synonyms)
'part of morpeth' is the wordplay.
'part of' indicates the answer is hidden within the clue.
'PET' is hidden in the letters of 'morpeth'.
(Other definitions for pet that I've seen before include "Tame animal kept for companionship" , "Favourite, perhaps a domestic animal" , "Little darling" , "Cherished animal" , "House animal; sulk" .)