Captain Kirk's starship business (10)
I believe the answer is:
enterprise
This clue is a double definition.
'captain kirk's starship' is the first definition.
(spaceship in Star Trek)
'business' is the second definition.
(enterprise can mean a business)
(Other definitions for enterprise that I've seen before include "Project, undertaking" , "Bold resourcefulness" , "audacity" , "Initiative - undertaking - business" , "Data may be on-board here" .)