To be exhausted after race not acceptable (3,3)
I believe the answer is:
run out
'to be exhausted' is the definition.
(eg a supply that has run out has been exhausted)
'after race not acceptable' is the wordplay.
'after' means one lot of letters go next to another.
'race' becomes 'run' (running is a kind of racing).
'not acceptable' becomes 'out' (cricket term).
'run' put next to 'out' is 'RUN OUT'.
(Other definitions for run out that I've seen before include "Dismiss (in cricket)" , "Come to an end" , "leak" , "Dismissed by a fielder" , "Dismissed (at cricket)" .)