I have to entertain duke absolutely (6)
I believe the answer is:
indeed
'absolutely' is the definition.
(both can be used to agree with something)
'i have to entertain duke' is the wordplay.
'have' becomes 'need' (synonyms).
'to entertain' is an insertion indicator.
'duke' becomes 'd' (abbreviation).
'need' enclosing 'd' is 'ndeed'.
'i'+'ndeed'='INDEED'
(Other definitions for indeed that I've seen before include "In reality" , "Surely" , "Yes, truthfully" , "''A friend in need is a friend . . . . . .''" , "Really - what a surprise!" .)