Waste product from home getting into river (5)
I believe the answer is:
urine
'waste product' is the definition.
(I know that urine is a type of body waste)
'home getting into river' is the wordplay.
'home' becomes 'in' ('he's home' can mean 'he's in').
'getting into' indicates putting letters inside.
'river' becomes 'ure' (river in Yorkshire).
'in' put within 'ure' is 'URINE'.
'from' acts as a link.
(Other definitions for urine that I've seen before include "Stuff that's passed" , "Water that one passes" , "Waste product" , "Wee" .)