Local girl's close shave (4,4)
I believe the answer is:
near miss
'close shave' is the definition.
'local girl's' is the wordplay.
'local' becomes 'near'.
'girl' becomes 'miss' (I've seen this before**).
'near'+'miss'='NEAR MISS'
(Other definitions for near miss that I've seen before include "Almost successful shot" , "Narrowly avoided collision, not quite on target (4, 4)" , "meeting thankfully avoided" , "Close to an accident" , "Almost a hit" .)