Use former conspiracy about Illuminati's leader (7)
I believe the answer is:
exploit
'use' is the definition.
(exploiting is a kind of using)
'former conspiracy about illuminati's leader' is the wordplay.
'former' becomes 'ex' (prefix meaning former or onetime).
'conspiracy' becomes 'plot' (I've seen this before).
'about' is an insertion indicator.
'leader' says to take the initial letters.
The initial letter of 'illuminatis' is 'i'.
'plot' going around 'i' is 'ploit'.
'ex'+'ploit'='EXPLOIT'
(Other definitions for exploit that I've seen before include "put to good use" , "Make full use of" , "Milk" , "Make use of - achievement" , "Make capital out of" .)