The most common and most likely answer to this crossword clue is the 5 plus 6 letter word CIVVY STREET
I've seen this crossword clue in The Times
C
I
V
V
Y
S
T
R
E
E
T
Buddy explains!
The straight part
We know that "Not a soldier’s way of life" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case not a soldier’s way of life = civvy street.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.