Oppressive individual, awake endlessly (7)
I believe the answer is:
onerous
'oppressive' is the definition.
(onerous can mean crushing or oppressive)
'individual awake endlessly' is the wordplay.
'individual' becomes 'one' (an individual is one person).
'awake endlessly' becomes 'rous' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'one'+'rous'='ONEROUS'
Can you help me to learn more?
(Other definitions for onerous that I've seen before include "Burdensome, heavy kind of duty" , "Effortful" , "Trying" , "Difficult, troublesome" , "Challenging" .)