The most common and most likely answer to this crossword clue is the 11 letter word BATTLEFIELD
I've seen this crossword clue in Independent
B
A
T
T
L
E
F
I
E
L
D
More clues leading to the result BATTLEFIELD
Buddy explains!

The straight part
We know that "Fight here" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fight here = battlefield.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 BATTLEFIELD mean?
BATTLEFIELD noun- The area where a land battle is or was fought, which is not necessarily a field.