After wine, political wings will accept that is arrogant (8)
I believe the answer is:
cavalier
'arrogant' is the definition.
(thesaurus)
'after wine political wings will accept that is' is the wordplay.
'after' means one lot of letters go next to another.
'wine' becomes 'cava' (type of Spanish wine).
'political wings' becomes 'LR' (abbreviations for left and right).
'will accept' indicates putting letters inside.
'that is' becomes 'ie' (short for Latin 'id est', 'that is').
'lr' going around 'ie' is 'lier'.
'cava'+'lier' is 'CAVALIER'.
(Other definitions for cavalier that I've seen before include "Herrick and Lovelace were such poets" , "Monarchist" , "English Civil War royalist" , "High-handed, supercilious" , "Casual" .)