Conversation doubly offensive about each EU leader (4-1-4)
I believe the answer is:
tete-a-tete
'conversation' is the definition.
(I know that tete-a-tete is a type of conversation)
'doubly offensive about each eu leader' is the wordplay.
'doubly' indicates the doubling of some letters.
'offensive' becomes 'tet' (Tet Offensive, Vietnam War military campaign).
'about' indicates putting letters inside.
'each' becomes 'ea' (abbreviation).
'leader' says to take the initial letters.
The first letter of 'eu' is 'e'.
'tet' doubled is 'tettet'.
'tettet' going around 'ea' is 'teteatet'.
'teteatet'+'e'='TETE-A-TETE'
(Other definitions for tete-a-tete that I've seen before include "Private couple's conversation" , "Private conversation between two people as in France" , "One-to-one meeting" , "Private conversation between two French people" , "Informal chat" .)