Anger dissipating about narrow, narrow escape (4,5)
I believe the answer is:
near thing
'narrow escape' is the definition.
(I've seen this before)
'anger dissipating about narrow' is the wordplay.
'dissipating' indicates an anagram.
'about' is an insertion indicator.
'narrow' becomes 'thin' ('thin' can be similar in meaning to 'narrow').
'anger' anagrammed gives 'nearg'.
'nearg' enclosing 'thin' is 'NEAR THING'.
(Other definitions for near thing that I've seen before include "Narrow escape, missed by a small margin (4.5)" , "Almost a nasty incident" , "Lucky escape" , "Narrow escape, close shave" , "Something that barely avoids failure or disaster" .)