Grotesque, having caught drunken expostulation (6)
I believe the answer is:
gothic
'grotesque' is the definition.
(thesaurus)
'caught drunken expostulation' is the wordplay.
'caught' becomes 'got' ('get' can be a synonym of 'catch').
'drunken expostulation' becomes 'hic' (I can't explain this - if you can you should believe this answer much more).
'got'+'hic'='GOTHIC'
'having' acts as a link.
Can you help me to learn more?
(Other definitions for gothic that I've seen before include "Style between Romanesque and Classical" , "Old-fashioned type" , "Style of e.g. Notre-Dame, Chartres" , "as some Germans were" , "Medieval architecture style" .)