Medical speciality doubled European understanding (7)
I believe the answer is:
entente
'understanding' is the definition.
(entente is a kind of understanding)
'medical speciality doubled european' is the wordplay.
'medical speciality' becomes 'ent' (abbreviation for Ear, Nose and Throat).
'doubled' shows that letters should be duplicated.
'european' becomes 'E' (abbreviation e.g. EU).
'ent' doubled is 'entent'.
'entent'+'e'='ENTENTE'
(Other definitions for entente that I've seen before include "Interstate understanding" , "Amicable agreement" , "Diplomatic agreement" , "friendly relations" , "Friendly alliance between states" .)