What the well-groomed man has is a narrow escape (5,5)
I believe the answer is:
close shave
'a narrow escape' is the definition.
(I've seen this before)
'what the well-groomed man has' is the wordplay.
I cannot quite see how this works, but
'man' could be 'ave' and 'ave' is present in the answer.
This may be the basis of the clue (or it may be nonsense).
'is' acts as a link.
Can you help me to learn more?
(Other definitions for close shave that I've seen before include "result being not so hairy" , "nasty moment" , "Narrow escape from disaster" , "Near thing" , "Sharp razor helps with this" .)