The most common and most likely answer to this crossword clue is the 5 plus 8 letter word STAFF OFFICERS
S
T
A
F
F
O
F
F
I
C
E
R
S
Buddy explains!
The straight part
We know that "They may serve general" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case they may serve general = staff officers.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.