After the pony, it may suggest a greyhound (4)
I believe the answer is:
trap
'it may suggest a greyhound' is the definition.
The definition suggests a singular noun which matches the answer.
'after the pony' is the wordplay.
'after' says to put letters next to each other.
'the' becomes 't' (the is pronounced as a 't' sound in some dialects).
'pony' becomes 'rap' (I can't justify this - if you can you should give a lot more credence to this answer).
't'+'rap' is 'TRAP'.
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" .)