King getting into Great British bitter (5)
I believe the answer is:
acerb
'bitter' is the definition.
(synonyms)
'king getting into great british' is the wordplay.
'king' becomes 'R' (abbreviation of Latin rex).
'getting into' is an insertion indicator.
'great' becomes 'ace' (ace can informally mean very good).
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'ace'+'b'='aceb'
'r' inserted inside 'aceb' is 'ACERB'.
(Other definitions for acerb that I've seen before include "sharp" , "Sour, bitter" , "harsh and bitter" , "tart" .)