To incite’s about right: rider’s put his foot in it? (7)
I believe the answer is:
stirrup
'rider's put his foot in it?' is the definition.
'to incite's about right' is the wordplay.
'to incite' becomes 'stirup' ('stir up' can be a synonym of 'incite').
'about' is an insertion indicator.
'right' becomes 'r' (common abbreviation).
'stirup' placed around 'r' is 'STIRRUP'.
(Other definitions for stirrup that I've seen before include "Small bone of the middle ear - it purrs (anag)" , "Small thing needed in hearing" , "Rider's foothold" , "Rider's footpiece" , "Equine foot rest" .)