Horse joke one's often heard (8)
I believe the answer is:
chestnut
'horse' is the definition.
(I know that chestnut is a type of horse)
I don't understand the remainder of the clue.
Can you help me to learn more?
(Other definitions for chestnut that I've seen before include "comedian's overused line?" , "Wood" , "Deep reddish-brown" , "Laughably predictable" , "Sweet -; horse -; water -" .)