A new curve is accompanied by medium lawlessness (9)
I believe the answer is:
anarchism
'lawlessness' is the definition.
Although both the answer and definition are singular nouns, I can't see how they can define each other.
'a new curve is accompanied by medium' is the wordplay.
'a new' becomes 'anarch' (I can't justify this - if you can you should give a lot more credence to this answer).
'curve' indicates anagramming the letters (I've seen 'curves' mean this).
'accompanied by' says to put letters next to each other.
'medium' becomes 'm' (as in UK clothing sizes).
'is' after 'm' is 'mis'.
'mis' is an anagram of 'ism'.
'anarch'+'ism'='ANARCHISM'
Can you help me to learn more?
(Other definitions for anarchism that I've seen before include "Bakunin advocated it" , "lawless attitude" , "Man's chair (anag.)" , "anti-government doctrine" , "Anti-government ideology" .)