Exasperate by ordering a race bet (8)
I believe the answer is:
acerbate
'exasperate' is the definition.
(I've seen this before)
'ordering a race bet' is the wordplay.
'ordering' indicates anagramming the letters.
'a'+'race'+'bet'='aracebet'
'aracebet' anagrammed gives 'ACERBATE'.
'by' acts as a link.
(Other definitions for acerbate that I've seen before include "Put out" , "Exasperate" , "distress" .)