Having put up fitting, chuck it down (4)
I believe the answer is:
teem
'chuck it down' is the definition.
(teem can mean to rain)
'having put up fitting' is the wordplay.
'having put up' says the letters should be written backwards (in a down clue, letters go up).
'fitting' becomes 'meet' (meet can mean appropriate or apt).
'meet' written backwards gives 'TEEM'.
(Other definitions for teem that I've seen before include "Pullulate" , "Swarm around meet" , "(Of rain) fall heavily" , "numerous" , "Abound, swarm with" .)