Fare cut the old American rejected? (4,4)
I believe the answer is:
chop suey
'fare' is the definition.
(chop suey is a kind of food)
'cut the old american rejected?' is the wordplay.
'cut' becomes 'chop' (chopping is a kind of cutting).
'the old' becomes 'ye' (resembles a historical spelling of 'the').
'american' becomes 'us' (abbreviation for United States).
'rejected?' says the letters should be written backwards.
'ye'+'us'='yeus'
'yeus' back-to-front is 'suey'.
'chop'+'suey'='CHOP SUEY'
(Other definitions for chop suey that I've seen before include "Might he copy us badly in this Chinese-style dish?" , "Chinese dish of stir-fried meat or fish with vegetables, originally created in the US" , "Chinese dish of meat pieces, rice and vegetables" , "Cue Sophy into Chinese dish of meat, rice and vegetables" .)