The most common and most likely answer to this crossword clue is the 11 letter word BATTLESHIPS
I've seen this crossword clue in The Sunday Telegraph
B
A
T
T
L
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Buddy explains!
The straight part
We know that "naval game" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case naval game = battleships.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 BATTLESHIPS mean?
BATTLESHIPS noun- Large capital warship displacing tens of thousands of tons, heavily armoured and armed with big guns. Battleships are now obsolescent, replaced by smaller vessels with guided missiles. Types: dreadnought, pre-dreadnought.
- Non-functional rocket stage, used for configuration and integration tests.
- A guessing game played on grid paper, see Battleship (game)