Run after a tyre burst in main road (6)
I believe the answer is:
artery
'main road' is the definition.
'run after a tyre burst' is the wordplay.
'run' becomes 'r' (cricket abbreviation).
'after' says to put letters next to each other.
'burst' indicates anagramming the letters.
'tyre' with letters rearranged gives 'tery'.
'r' after 'a' is 'ar'.
'ar'+'tery'='ARTERY'
'in' acts as a link.
(Other definitions for artery that I've seen before include "Main traffic route" , "Major traffic route" , "bloody path" , "Principle channel of circulatory system" , "Something that could be clogged" .)