The most common and most likely answer to this crossword clue is the 5 plus 5 letter word CLOSE SHAVE
I've seen this crossword clue in Independent
C
L
O
S
E
S
H
A
V
E
More clues leading to the result CLOSE SHAVE
- Seals experience narrow escape
- Narrow escape as Charlie evades bear
- Fail to keep quiet in underground chamber, making narrow escape
- Ends with experience from near disaster
- Shuts road after Henry’s narrow escape
- Terrible chaos with elves in narrow escape
- Shuts short road after hospital’s lucky escape
- Near thing becomes near ting? Be careful about it
- Narrow escape — from a cut-throat?
- Narrow escape — from cutting it fine?
Buddy explains!

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.