Outrage seeing 'fake news' contains nothing (7)
I believe the answer is:
dudgeon
'outrage' is the definition.
(dudgeon is a kind of outrage)
'fake news contains nothing' is the wordplay.
'fake' becomes 'dud' (I am not sure about this - if you are sure you should believe this answer much more).
'news' becomes 'gen'.
'contains' means one lot of letters goes inside another.
'nothing' becomes 'o' (looks like zero - 0).
'gen' placed around 'o' is 'geon'.
'dud'+'geon'='DUDGEON'
'seeing' acts as a link.
Can you help me to learn more?
(Other definitions for dudgeon that I've seen before include "(High) resentment" , "Feeling of intense indignation" , "Devil's Disciple" , "Offended indignation" , "State of being (highly) aggrieved" .)