Reportedly, put out to search for water (5)
I believe the answer is:
dowse
'search for water' is the definition.
(as in using a dowsing rod)
'reportedly put out' is the wordplay.
'reportedly' shows a homophone (sound like).
'put out' becomes 'douse' (as in to douse a fire).
'douse' sounds like 'DOWSE'.
'to' acts as a link.
(Other definitions for dowse that I've seen before include "try to find water" , "Prospect for water" , "Use a divining rod" , "twitch" , "Detect underground water" .)