With the current duke, have new master (10)
I believe the answer is:
downstream
'with the current' is the definition.
(I've seen this before)
'duke have new master' is the wordplay.
'duke' becomes 'd'.
'have' becomes 'own' ('own' can be a synonym of 'have').
'new' indicates an anagram.
'master' anagrammed gives 'stream'.
'd'+'own'+'stream'='DOWNSTREAM'
(Other definitions for downstream that I've seen before include "Further along in the flow" , "With the current" , "direction?" .)