Award originally conveyed on horseback (3)
I believe the answer is:
cup
'award' is the definition.
(I've seen this in other clues)
'originally conveyed on horseback' is the wordplay.
'originally' indicates taking the first letters.
'on horseback' becomes 'up' (up can mean up on a horse).
The initial letter of 'conveyed' is 'c'.
'c'+'up'='CUP'
(Other definitions for cup that I've seen before include "Beaker" , "Trophy; drinking vessel" , "Prize; vessel" , "Sort of cake" , "competition" .)