The most common and most likely answer to this crossword clue is the 7 plus 1 plus 7 letter word BEATING A RETREAT
I've seen this crossword clue in Financial Times
B
E
A
T
I
N
G
A
R
E
T
R
E
A
T
Buddy explains!
The straight part
We know that "running from battle" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case running from battle = beating a retreat.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.