Highlight organised demonstration's centrepiece being outrageous (8)
I believe the answer is:
flagrant
'outrageous' is the definition.
(flagrant can mean outrageous or blatant)
'highlight organised demonstration's centrepiece' is the wordplay.
'highlight' becomes 'flag' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'organised' becomes 'ran' (run can mean to manage or organise).
'demonstration' becomes 'protest' (I have seen 'Public demonstration ' mean 'protest' so perhaps 'demonstration' could also mean 'protest').
'centrepiece' indicates the central letters (the letter at the centre).
The middle letter of 'protest' is 't'.
'flag'+'ran'+'t'='FLAGRANT'
'being' acts as a link.
Can you help me to learn more?
(Other definitions for flagrant that I've seen before include "Being shameless" , "Conspicuous, blatant" , "Barefaced" , "notorious" , "Patent" .)