Duke has Barnaby as a servant (6)
I believe the answer is:
drudge
'a servant' is the definition.
(I have seen 'Menial servant' mean 'drudge' so perhaps 'servant' could also mean 'drudge')
'duke has barnaby' is the wordplay.
'duke' becomes 'd'.
'has' says to put letters next to each other.
'barnaby' becomes 'rudge' (barnaby rudge is a dickens novel).
'd'+'rudge'='DRUDGE'
'as' is the link.
(Other definitions for drudge that I've seen before include "Menial servant" , "One works hard at boring tasks" , "Doer of hard dull work" , "One who is obliged to do menial work" , "One does long and boring work" .)