Comes out of European Union, mostly with backing of idiots (7)
I believe the answer is:
emerges
'comes out' is the definition.
('emerge' can be a synonym of 'come out')
'european union mostly with backing of idiots' is the wordplay.
'european union' becomes 'eu'.
'mostly' means to remove the last letter.
'with' means one lot of letters go next to another.
'backing of idiots' becomes 'merges' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'eu' with its final letter taken away is 'e'.
'e'+'merges'='EMERGES'
'of' is the link.
Can you help me to learn more?
(Other definitions for emerges that I've seen before include "Turns out" , "Issues" , "appears" , "Comes out" .)