Little half coughs significant in the navy (3)

I believe the answer is:

hms

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'significant in the navy' is the definition.
I can't tell whether this definition defines the answer.

'little half coughs' is the wordplay.
'little' indicates taking the first letters.
'coughs' becomes 'ms' (I am not sure about this - if you are sure you should believe this answer much more).
The first letter of 'half' is 'h'.
'h'+'ms'='HMS'

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