Disaster averted by your neighbour's phoning you? (5,4)
I believe the answer is:
close call
'disaster averted by your' is the definition.
I can't judge whether this defines the answer.
'neighbour's phoning you?' is the wordplay.
'neighbour' becomes 'close' (similar in meaning).
'phoning you?' becomes 'call' (I can't justify this - if you can you should believe this answer much more).
'close'+'call'='CLOSE CALL'
Can you help me to learn more?
(Other definitions for close call that I've seen before include "One may be disputed in court" , "Narrow squeak" , "hang up" , "Lucky escape" , "Narrow decision" .)