The most common and most likely answer to this crossword clue is the 8 letter word CIVILIAN
I've seen this crossword clue in The Times
C
I
V
I
L
I
A
N
Buddy explains!
The straight part
We know that "One not serving" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one not serving = civilian.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 CIVILIAN mean?
CIVILIAN noun- A person following the pursuits of civil life, especially one who is not an active member of the armed forces.
- A person who does not belong to a particular group or engage in a particular activity.
- One skilled in civil law.
- A student of civil law at a university or college.
- Not related to the military, police or other professions.