Inept cowboy finally going east (6)
I believe the answer is:
gauche
'inept' is the definition.
(gauche means socially inept or awkward)
'cowboy finally going east' is the wordplay.
'cowboy' becomes 'gaucho' (term for a South American cowboy).
'finally going' means to remove the last letter (the final letter is removed).
'east' becomes 'e' (abbreviation).
'gaucho' with its last letter removed is 'gauch'.
'gauch'+'e'='GAUCHE'
(Other definitions for gauche that I've seen before include "not right for Parisian" , "Tactless - blundering" , "Awkward, inept" , "Graceless" , "Ill-at-ease, awkward in social situations" .)