The most common and most likely answer to this crossword clue is the 5 plus 3 letter word CLEAN CUT
I've seen this crossword clue in The Guardian
C
L
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A
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More clues leading to the result CLEAN CUT
Buddy explains!
The straight part
We know that "Smart/surgeon’s initial priority" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case smart/surgeon’s initial priority = clean cut.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.
What does CLEAN CUT mean?
CLEAN CUT adjective- Having a neat, smart appearance