Academy that houses folklore (4)
I believe the answer is:
myth
'folklore' is the definition.
(thesaurus)
'academy that houses' is the wordplay.
'houses' indicates the answer is hidden within the clue (part of the clue houses the answer).
'MYTH' can be found hidden inside 'academy that'.
(Other definitions for myth that I've seen before include "A US president; a UK PM" , "Wildly-held but false belief or idea" , "Ancient story" , "Delusion" , "A widely held but false belief" .)