Sap duke’s yearning (5)
I believe the answer is:
ditch
'sap' is the definition.
(thesaurus)
'duke's yearning' is the wordplay.
'duke' becomes 'd' (abbreviation).
'yearning' becomes 'itch' (I've seen this in another clue).
'd'+'itch'='DITCH'
(Other definitions for ditch that I've seen before include "Throw away (sl.)" , "Dyke" , "long depression" , "Abandon; one dug" , "side of field?" .)