Man in posh car running into horse (5)
I believe the answer is:
barry
'man' is the definition.
'posh car running into horse' is the wordplay.
'posh car' becomes 'rr' (short for Rolls Royce).
'running into' indicates putting letters inside.
'horse' becomes 'bay' (bay is a kind of horse).
'rr' put within 'bay' is 'BARRY'.
'in' acts as a link.
(Other definitions for barry that I've seen before include "South Wales town -- boy's name" , "-- Island, Welsh resort" .)