Local turns up with one on horse (4)
I believe the answer is:
arab
'horse' is the definition.
(Arab is an example)
'local turns up with one' is the wordplay.
'local' becomes 'bar' (I've seen this before).
'turns up' is a reversal indicator.
'with' says to put letters next to each other.
'one' becomes 'a'.
'bar' backwards is 'rab'.
'rab' after 'a' is 'ARAB'.
'on' acts as a link.
(Other definitions for arab that I've seen before include "race" , "Horse of a breed originating in the Middle East" , "Semite" , "Someone from the Middle East or North Africa, perhaps" , "One from Saudi" .)