Perhaps Carmen's old fruit hat stripped down to the base (5)
I believe the answer is:
opera
'perhaps carmen's' is the definition.
(Carmen is an example)
I don't understand the remainder of the clue.
Can you help me to learn more?
(Other definitions for opera that I've seen before include "Eg, Il trovatore" , "Stage entertainment" , "Eg, La traviata" , "Carmen, for instance" , "Norma is one" .)