Duke has desire for drainage channel (5)
I believe the answer is:
ditch
'drainage channel' is the definition.
(I've seen this before)
'duke has desire' is the wordplay.
'duke' becomes 'd' (abbreviation).
'has' means one lot of letters go next to another.
'desire' becomes 'itch' (itch is a kind of desire).
'd'+'itch'='DITCH'
'for' acts as a link.
(Other definitions for ditch that I've seen before include "Moat" , "Drainage trench" , "Abandon; one dug" , "Narrow channel" , "Throw away (sl.)" .)