Exhausted American editor on horseback (4,2)
I believe the answer is:
used up
'exhausted' is the definition.
('used-up' can be similar in meaning to 'exhausted')
'american editor on horseback' is the wordplay.
'american' becomes 'us'.
'editor' becomes 'ed'.
'on horseback' becomes 'up'.
'us'+'ed'+'up'='USED-UP'
(Other definitions for used up that I've seen before include "Consumed, finished" , "Exhausted the supply" , "Consumed completely" , "Spent" .)