Publish landlord's overseas correspondence (3,6)
I believe the answer is:
air letter
'overseas correspondence' is the definition.
'publish landlord's' is the wordplay.
'publish' becomes 'air' (I've seen this before).
'landlord' becomes 'letter' (landlords let property).
'air'+'letter'='AIR LETTER'
(Other definitions for air letter that I've seen before include "Item of overseas mail" , "speedy delivery" , "Item of overseas post" .)