Arrogant PM to pursue crazy American (12)
I believe the answer is:
presumptuous
'arrogant' is the definition.
(thesaurus)
'pm to pursue crazy american' is the wordplay.
'crazy' indicates an anagram.
'american' becomes 'us'.
'pm'+'to'+'pursue'='pmtopursue'
'pmtopursue' is an anagram of 'presumptuo'.
'presumptuo'+'us'='PRESUMPTUOUS'
(Other definitions for presumptuous that I've seen before include "Bold - forward" , "Impertinently bold" , "Assuming too much" , "Impertinent" .)