There's a Terrible Russian vehicle after me! (4)
I believe the answer is:
ivan
'there's a terrible russian' is the definition.
(Ivan the Terrible)
'vehicle after me' is the wordplay.
'vehicle' becomes 'van' (type of vehicle).
'after' says to put letters next to each other.
'me' becomes 'I'.
'van' after 'i' is 'IVAN'.
(Other definitions for ivan that I've seen before include "terrible tyrant" , "Russian ruler - a Terrible one" , "One Day in the Life of - Denisovich (Solzhenitsyn)" , "First Russian tsar, 1547-84" , "__ Lendl, Czech-born American tennis star" .)