Costly address to partner (4)
I believe the answer is:
dear
I believe this clue is a double definition.
'costly' is the first definition.
('dear' can be a synonym of 'costly')
'address to partner' is the second definition.
(term of endearment)
(Other definitions for dear that I've seen before include "At a high cost" , "polite form of address" , "Honey - costly" , "Baby" , "Beloved - expensive" .)