Reportedly unproductive bodily vessel (4)
I believe the answer is:
vein
'bodily vessel' is the definition.
'vein' can be an answer for 'vessel' (vein is a kind of vessel). I'm unsure of the 'bodily' bit.
'reportedly unproductive' is the wordplay.
'reportedly' indicates a 'sounds like' (homophone) clue.
'unproductive' becomes 'vain' (similar in meaning).
'vain' sounds like 'VEIN'.
Can you help me to learn more?
(Other definitions for vein that I've seen before include "Blood-carrying vessel" , "Vessel for claret" , "Leaf rib; ore layer in rock" , "Vessel carrying blood towards the heart" , "Deposit of mineral" .)