Cook run into by duke’s open car (8)
I believe the answer is:
roadster
'open car' is the definition.
(type of open-top car)
'cook run into by duke's' is the wordplay.
'cook' becomes 'roaster' (someone who roasts).
'run into by' indicates putting letters inside (some letters run into others).
'duke' becomes 'd' (abbreviation).
'roaster' enclosing 'd' is 'ROADSTER'.
(Other definitions for roadster that I've seen before include "An open car without rear seats" , "Open-topped car" , "Old car" , "Small open-top car" , "sporty vehicle" .)