English regret getting upset about chief American card game (6)
I believe the answer is:
euchre
'american card game' is the definition.
(I've seen this before)
'english regret getting upset about chief' is the wordplay.
'english' becomes 'e' (abbreviation).
'regret' becomes 'rue' (synonyms).
'getting upset' says the letters should be written in reverse.
'about' is an insertion indicator.
'chief' becomes 'ch' (abbreviation).
'e'+'rue'='erue'
'erue' reversed gives 'eure'.
'eure' enclosing 'ch' is 'EUCHRE'.
(Other definitions for euchre that I've seen before include "Game of cards" , "card game in Chicago?" , "American card game" , "Outwit" , "American card-game" .)