News church rejected: it’s unusual article for the illuminati (14)
I believe the answer is:
intelligentsia
'the illuminati' is the definition.
(both can mean a group of influential intellectuals)
'news church rejected it's unusual article' is the wordplay.
'news' becomes 'intelligence' (intelligence can mean news or information).
'church' becomes 'CE' (abbreviation for Church of England).
'rejected' indicates named letters should be taken away.
'unusual article' becomes 'ia' (I can't explain this - if you can you should believe this answer much more).
'intelligence' with 'ce' taken away is 'intelligen'.
'intelligen'+'ts'+'ia'='INTELLIGENTSIA'
'for' is the link.
(Other definitions for intelligentsia that I've seen before include "academics" , "Learned people" , "Scholarly types" , "thinkers" , "Eggheads" .)