Supporter heading west astride a horse (4)
I believe the answer is:
arab
'horse' is the definition.
(Arab is an example)
'supporter heading west astride a' is the wordplay.
'supporter' becomes 'bra' (a bra gives support to breasts).
'heading west' says the letters should be written backwards.
'astride' indicates putting letters inside.
'bra' back-to-front is 'arb'.
'arb' going around 'a' is 'ARAB'.
(Other definitions for arab that I've seen before include "Native of North Africa" , "Saudi, perhaps - breed of horse" , "One from the Middle East or North Africa" , "race" , "One from Saudi" .)