Petite flyer no man in Royal Navy (4)
I believe the answer is:
wren
I believe this is a double definition.
'petite flyer' is the first definition.
'no man in royal navy' is the second definition.
(historic term for woman in the Royal Navy)
(Other definitions for wren that I've seen before include "Former RN woman" , "Small bird - great architect" , "held up by wings at small scale?" , "flier" , "Tiny bird" .)