Rain heavily as hunting party turning up (4)
I believe the answer is:
teem
'rain heavily' is the definition.
(I've seen this before)
'hunting party turning up' is the wordplay.
'hunting party' becomes 'meet'.
'turning up' says the letters should be written in reverse.
'meet' backwards is 'TEEM'.
'as' acts as a link.
(Other definitions for teem that I've seen before include "Be prolific" , "Be swarming (with)" , "(Of rain) pour down" , "Seethe" , "Rain buckets" .)