Refuge is famously out of fashion (6)
I believe the answer is:
asylum
'refuge' is the definition.
(synonyms)
'famously out of fashion' is the wordplay.
'out' suggests deleting specific letters.
'fashion' indicates an anagram.
'famously' with 'of' taken out is 'amusly'.
'amusly' anagrammed gives 'ASYLUM'.
'is' acts as a link.
(Other definitions for asylum that I've seen before include "Refuge or home for mentally ill" , "A shelter from danger or hardship" , "Place of refuge, once a mental institution" , "Shelter for refugees" , "find sanctuary there" .)