The most common and most likely answer to this crossword clue is the 13 plus 8 letter word CONSCIENTIOUS OBJECTOR
I've seen this crossword clue in The Times
C
O
N
S
C
I
E
N
T
I
O
U
S
O
B
J
E
C
T
O
R
Buddy explains!
The straight part
We know that "One refusing to serve" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one refusing to serve = conscientious objector.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.