Clumsy cowboy not entirely on horse's back (6)
I believe the answer is:
gauche
'clumsy' is the definition.
(gauche means socially awkward or clumsy)
'cowboy not entirely on horse's back' is the wordplay.
'cowboy' becomes 'gaucho' (gaucho is a kind of cowboy).
'not entirely' means to remove the last letter.
'on horse's back' becomes 'e' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'gaucho' with its final letter taken off is 'gauch'.
'gauch'+'e'='GAUCHE'
(Other definitions for gauche that I've seen before include "Unsophisticated and socially awkward" , "Clumsily tactless" , "Awkward in manner, tactless" , "inelegant" , "Graceless" .)