Heavy drinker getting very rich (4)
I believe the answer is:
lush
I believe this clue is a double definition.
'heavy drinker' is the first definition.
(I've seen this before)
'very rich' is the second definition.
(I've seen this in another clue)
'getting' acts as a link.
(Other definitions for lush that I've seen before include "Of growth, profuse and abundant" , "dipsomaniac?" , "Succulent - heavy drinker" , "Green and growing abundantly" , "sponge" .)