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