Colour of barrel upset by British private (8)
I believe the answer is:
nutbrown
'colour' is the definition.
(shade of brown)
'barrel upset by british private' is the wordplay.
'barrel' becomes 'tun' (tun is a kind of barrel).
'upset' says the letters should be written in reverse.
'by' is a charade indicator (letters next to each other).
'british' becomes 'br'.
'private' becomes 'own' (as in one's own or private belongings).
'tun' backwards is 'nut'.
'nut'+'br'+'own'='NUTBROWN'
'of' is the link.
(Another definition for nutbrown that I've seen is " The colour of a ripe cob".)