Oil-drilling structure (3)
I believe the answer is:
'oil-drilling structure' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for rig that I've seen before include "Outfit of clothes or oil-drilling platform" , "Masts, spars and sails on a vessel" , "Apparatus; fix" , "set-up" , "Gear; fiddle" .)