After the pony, it may suggest a greyhound (4)
I believe the answer is:
trap
'a greyhound' is the definition.
Although both the answer and definition are singular nouns, I can't see how one could define the other.
'after the pony it' is the wordplay.
I cannot really see how this works, but
'it' could be 't' (abbreviation. e.g. in 'tis) and 't' is found in the answer.
The remaining letters 'rap' is a valid word which might be clued in a way I don't see.
This may be the basis of clue (or it may be nonsense).
'may suggest' acts as a link.
Can you help me to learn more?
(Other definitions for trap that I've seen before include "ladder" , "mug" , "Pitfall" , "Part of a snare" , "Ambush" .)