Expose cover after sister removes hat (8)
I believe the answer is:
unclothe
'expose' is the definition.
(I know that unclothe is a more specific form of expose)
'cover after sister removes hat' is the wordplay.
'cover' becomes 'clothe' (synonyms).
'after' is a charade indicator (letters next to each other).
'sister' becomes 'nun' (sister is a term of address for a nun).
'removes hat' means to remove the first letter (I've seen 'removing hat' mean this (the top letter or 'hat' is removed)).
'nun' with its first letter removed is 'un'.
'clothe' put after 'un' is 'UNCLOTHE'.
(Other definitions for unclothe that I've seen before include "Strip (someone)" , "lay bare" , "Disrobe" , "shed" , "Reveal" .)