Has a reputation for exposing type of philosophy that's not in favour of cover-up (6)
I believe the answer is:
nudism
'favour of cover-up' is the definition.
The answer and definition can be both acts as well as being singular nouns.
Perhaps you can see an association between them that I don't see?
'has a reputation for exposing type of philosophy that's not' is the wordplay.
I cannot really see how this works, but
'philosophy' could be 'ism' ('ism' can be a synonym of 'philosophy') and 'ism' is present in the answer.
This explanation may well be incorrect...
'in' acts as a link.
Can you help me to learn more?
(Other definitions for nudism that I've seen before include "Practice of going naked" , "early practice in Eden" , "Having nothing on" , "Pursuit of a naturist" , "taking off habitually" .)