See me backing horse entered in Derby for example (6)
I believe the answer is:
eponym
'see me backing' is the definition.
Although both the answer and definition are singular nouns, I can't see how they can define each other.
'horse entered in derby for example' is the wordplay.
'horse' becomes 'pony' (pony is a kind of horse).
'entered in' means one lot of letters goes inside another.
'derby for example' becomes 'em' (I can't justify this - if you can you should believe this answer much more).
'pony' inserted into 'em' is 'EPONYM'.
Can you help me to learn more?
(Other definitions for eponym that I've seen before include "a mackintosh, for instance" , "Distinguishing title; derived name" , "Hero" , "eg 'Jane Eyre'" , "Name derived from title etc." .)