Petite flier no man in Navy (4)
I believe the answer is:
wren
'petite flier' is the definition.
'wren' can be an answer for 'flier' (wren is a kind of birdanimal). I am not sure about the 'petite' bit.
'no man in navy' is the wordplay.
'no' becomes 'we' (I can't explain this - if you can you should give a lot more credence to this answer).
'man' becomes 'r' (abbreviation for rook, a chess piece or 'man').
'in' indicates putting letters inside.
'navy' becomes 'N' (common abbreviation eg in RN Royal Navy).
'we' placed around 'r' is 'wre'.
'wre'+'n'='WREN'
Can you help me to learn more?
(Other definitions for wren that I've seen before include "held up by wings at small scale?" , "Tiny brown songbird with a short upright tail" , "of two wings?" , "Small singer" , "one leaving evidence all around London monument" .)