Primate backing big toff from the east? (6)
I believe the answer is:
gibbon
'primate' is the definition.
(gibbon is a kind of primate)
'backing big toff from the east?' is the wordplay.
'backing' is a reversal indicator.
'toff' becomes 'nob' (UK slang for a wealthy or upper-class person).
'from the east?' says the letters should be written in reverse (I've seen 'from the east' mean this).
'big' backwards is 'gib'.
'nob' reversed gives 'bon'.
'gib'+'bon'='GIBBON'
(Other definitions for gibbon that I've seen before include "author of Decline and Fall, etc" , "Writer" , "Primate" , "an eighteenth-century author" , "A historian; SE Asian forest creature" .)