A week following central element in cult is hideous (5)
I believe the answer is:
awful
'hideous' is the definition.
(thesaurus)
'a week following central element in cult' is the wordplay.
'week' becomes 'w' (abbreviation).
'following' becomes 'f.' (used when citing page numbers etc).
'central element in' indicates the central letters.
The middle letters of 'cult' are 'ul'.
'a'+'w'+'f'+'ul'='AWFUL'
'is' is the link.
(Other definitions for awful that I've seen before include "Horrific" , "gruesome!" , "Horrible" , "Dreadful - spine-chilling" , "Dreadful, really bad" .)