Largely inept contractor's number two is cowboy (6)
I believe the answer is:
gaucho
'is cowboy' is the definition.
(term for a South American cowboy)
'largely inept contractor's number two' is the wordplay.
'largely' means to remove the last letter.
'inept' becomes 'gauche' (gauche means socially inept or awkward).
'contractor's number two' becomes 'o' (2nd letter of 'contractor').
'gauche' with its last letter taken away is 'gauch'.
'gauch'+'o'='GAUCHO'
(Other definitions for gaucho that I've seen before include "Plain-living person" , "foreign cowhand" , "plainsman" , "Cowboy of Argentine's plains" , "Horseman of the Pampas" .)