Italian author capturing husband's parrot (4)
I believe the answer is:
echo
'parrot' is the definition.
(both can mean to imitate or copy)
'italian author capturing husband's' is the wordplay.
'italian author' becomes 'eco' (Umberto Eco).
'capturing' means one lot of letters goes inside another.
'husband' becomes 'h' (abbreviation).
'eco' going around 'h' is 'ECHO'.
(Other definitions for echo that I've seen before include "Close imitation" , "One who slavishly copies" , "What evokes memories" , "Repetition by reflection" , "ring" .)