Rider's work had dropped (4)
I believe the answer is:
shed
'dropped' is the definition.
('shed' can be a synonym of 'drop')
'rider's work had' is the wordplay.
'rider's work' becomes 'she' (I can't justify this - if you can you should give a lot more credence to this answer).
'had' becomes 'd' (in contractions e.g. 'I'd', 'you'd' etc).
'she'+'d'='SHED'
Can you help me to learn more?
(Other definitions for shed that I've seen before include "Discard; small building" , "Abandoned" , "Dump" , "Throw off; building" , "something at the bottom of the garden?" .)