Sweet beauty accompanies bishop in Asian festival (5,5)
I believe the answer is:
peach melba
'sweet' is the definition.
(I've seen this before)
'beauty accompanies bishop in asian festival' is the wordplay.
'beauty' becomes 'peach' (synonyms).
'accompanies' means one lot of letters go next to another.
'bishop' becomes 'B' (abbreviation for bishop in chess).
'in' indicates putting letters inside.
'asian festival' becomes 'mela' (type of Hindu festival).
'b' going into 'mela' is 'melba'.
'peach'+'melba'='PEACH MELBA'
(Other definitions for peach melba that I've seen before include "Ice cream dish with fruit" , "fruity dessert" , "Dame Nellie's dish" , "Sweet" .)