Horse and buggy (3)
I believe the answer is:
'horse and buggy' 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 "Provide with clothes - for oil well?" , "Oil-drilling device" , "Outfit of clothes or oil-drilling platform" , "Manipulate; gear" , "Apparatus; outfit" .)