Wag's partner has Italian dress (5)
I believe the answer is:
habit
'dress' is the definition.
(I know this)
'wag's partner has italian' is the wordplay.
'wag's partner' becomes 'hab' (HAB is husband and boyfriends - equivalent to WAG).
'has' says to put letters next to each other.
'italian' becomes 'it' (abbreviation for Italian).
'hab'+'it'='HABIT'
(Other definitions for habit that I've seen before include "Custom, wont" , "It's worn in order" , "bent" , "Custom or monk's robe" , "Breaking this is hard" .)