A politician is carried by steed running in mad rush (8)
I believe the answer is:
stampede
'mad rush' is the definition.
(I've seen this before)
'a politician is carried by steed running' is the wordplay.
'politician' becomes 'mp' (Member of Parliament).
'is carried by' indicates putting letters inside.
'running' indicates an anagram.
'a'+'mp'='amp'
'steed' with letters rearranged gives 'stede'.
'amp' going within 'stede' is 'STAMPEDE'.
'in' is the link.
(Other definitions for stampede that I've seen before include "Sudden rush of frightened animals" , "Panicky run" , "A flight of frightened cattle" , "Headlong rush of a group in panic" , "Put to flight" .)