Frivolous layer, reportedly underwear (9)
I believe the answer is:
petticoat
'underwear' is the definition.
(I know that petticoat is a type of underwear)
'frivolous layer reportedly' is the wordplay.
I cannot really see how this works, but
'layer' could be 'coat' (I have seen 'Layer of paint' mean 'coat' so perhaps 'layer' could also mean 'coat') and 'coat' is found within the answer.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for petticoat that I've seen before include "Woman's underskirt" , "Female undergarment" , "Slip" , "London Lane" , "Woman's undergarment" .)