The most common and most likely answer to this crossword clue is the 4 plus 5 letter word NEAR THING
I've seen this crossword clue in Independent
N
E
A
R
T
H
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N
G
More clues leading to the result NEAR THING
- Improving electrical safety after new close shave
- Close call after finding that principal has left
- Anger dissipating about narrow, narrow escape
- Note, connecting the green wire is almost a disaster
- Northern gent with hair cut and close shave
- Northern person abandoning Hull in the end? It almost happens!
- Knight, with obsession for Listener, in close shave
- Armageddon: Earth in grief, not entirely a lucky escape?
- Dodgy event that is right under your eyes?
- Lucky escape: electrician finally making circuit safe
Buddy explains!

The straight part
We know that "close shave" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case close shave = near thing.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.