Narrowly avoided collision beside a lady (4,4)
I believe the answer is:
near miss
'narrowly avoided collision' is the definition.
(I've seen this before)
'beside a lady' is the wordplay.
'beside' becomes 'near' (I've seen this in another clue).
'a lady' becomes 'miss' (I have seen 'Young lady' mean 'miss' so perhaps 'lady' could also mean 'miss').
'near'+'miss'='NEAR MISS'
(Other definitions for near miss that I've seen before include "Almost hitting the target" , "Close to the target, just a little off" , "Narrowly avoided collision, not quite on target (4, 4)" , "Close thing" , "meeting thankfully avoided" .)