Near thing (5,5)
I believe the answer is:
close shave
'near thing' is the definition.
(I've seen this before)
This is the entire clue.
(Other definitions for close shave that I've seen before include "Chases vole (anag.)" , "nasty moment" , "result being not so hairy" , "Sharp razor helps with this" , "resulting in barefaced cheek?" .)