Friendly understanding hospital department twice exploited at first (7)
I believe the answer is:
entente
'friendly understanding' is the definition.
(I've seen this before)
'hospital department twice exploited at first' is the wordplay.
'hospital department' becomes 'ENT' (abbreviation for Ear, Nose and Throat department).
'twice' shows that letters should be duplicated.
'at first' indicates taking the first letters.
The initial letter of 'exploited' is 'e'.
'ent' duplicated is 'entent'.
'entent'+'e'='ENTENTE'
(Other definitions for entente that I've seen before include "Friendly understanding between states" , "Amicable agreement" , "Friendly agreement between countries" , "friendly relations" , "Informal alliance" .)