Looter overlooking a person on horseback (5)
I believe the answer is:
rider
'person on horseback' is the definition.
(someone riding a horse)
'looter overlooking a' is the wordplay.
'looter' becomes 'raider' (synonyms).
'overlooking' indicates named letters should be taken away.
'raider' with 'a' removed is 'RIDER'.
(Other definitions for rider that I've seen before include "Horseman or cyclist" , "Motorcyclist" , "Additional bit" , "Condition added to a legislative bill" , "Stipulation" .)