Irish can act riotously, wanting no form of government (11)
I believe the answer is:
anarchistic
'wanting no form of government' is the definition.
'irish can act riotously' is the wordplay.
'riotously' indicates anagramming the letters.
'irish'+'can'+'act'='irishcanact'
'irishcanact' is an anagram of 'ANARCHISTIC'.
(Other definitions for anarchistic that I've seen before include "Revolutionary" , "out of control" , "Like one wanting to overthrow government" , "lacking law and order" , "As unruly type" .)