Turn down European or US coin (4)
I believe the answer is:
dime
'us coin' is the definition.
(US coin worth ten cents)
'turn down european' is the wordplay.
'turn down' becomes 'dim' (I've seen this in another clue).
'european' becomes 'E' (abbreviation e.g. EU).
'dim'+'e'='DIME'
'or' acts as a link.
(Other definitions for dime that I've seen before include "US 10 cent coin" , "Ten US cents" , "Ten-cent coin in America" , "Something round and silvery" , "One tenth of a US dollar" .)