Horse's food supply began so oddly (7)
I believe the answer is:
nosebag
'horse's food' is the definition.
Although both the answer and definition are singular nouns, I can't see how they can define each other.
'began so oddly' is the wordplay.
'oddly' indicates anagramming the letters (letters in an odd order).
'began'+'so'='beganso'
'beganso' with letters rearranged gives 'NOSEBAG'.
'supply' is the link.
Can you help me to learn more?
(Other definitions for nosebag that I've seen before include "Horse's feed container" , "Container for a horse's dinner" , "Suspended food supply" , "Horse fodder holder" , "Feeder strapped on horse" .)