Parrot shy about pelican at first (4)
I believe the answer is:
copy
'parrot' is the definition.
(I've seen this in another clue)
'shy about pelican at first' is the wordplay.
'shy' becomes 'coy' (coy can mean shy or modest).
'about' means one lot of letters goes inside another.
'at first' says to take the initial letters.
The initial letter of 'pelican' is 'p'.
'coy' enclosing 'p' is 'COPY'.
(Other definitions for copy that I've seen before include "what's to be printed" , "Duplicate" , "Fake" , "Emulate, ape" , "transcription" .)