Supported leaving Europe, won unexpectedly - step away from the brink (4,4)
I believe the answer is:
back down
'step away from the brink' is the definition.
I can't judge whether this defines the answer.
'supported leaving europe won unexpectedly' is the wordplay.
'supported' becomes 'backed' (similar in meaning).
'leaving' suggests deleting specific letters.
'europe' becomes 'E' (abbreviation eg in E number).
'won unexpectedly' becomes 'own' (I can't justify this - if you can you should believe this answer much more).
'backed' with 'e' removed is 'backd'.
'backd'+'own'='BACK DOWN'
Can you help me to learn more?
(Other definitions for back down that I've seen before include "being in lower division once more?" , "Avoid a challenge - face up?" , "Withdraw argument in face of opposition" , "Give up claim or withdraw argument" , "Withdraw challenge" .)