Painter shot by half-cut American (4)
I believe the answer is:
goya
'painter' is the definition.
(thesaurus)
'shot by half-cut american' is the wordplay.
'shot' becomes 'go' (I've seen this in other clues**).
'half cut' indicates taking half.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'by' with half the letters taken is 'y'.
'go'+'y'+'a'='GOYA'
(Other definitions for goya that I've seen before include "Spanish painter, d. 1828" , "Portrait painter" , "Eighteenth and nineteenth century Spanish painter" , "Ay, go to see great Spanish painter" , "He painted Wellington" .)