A duke keeping goddess entertained (6)
I believe the answer is:
amused
'entertained' is the definition.
(amusing is a kind of entertaining)
'a duke keeping goddess' is the wordplay.
'duke' becomes 'd'.
'keeping' indicates putting letters inside.
'goddess' becomes 'muse' (I've seen this in other clues**).
'a'+'d'='ad'
'ad' going around 'muse' is 'AMUSED'.
(Other definitions for amused that I've seen before include "Delighted" , "Provoked mirth in" , "Mildly diverted or entertained" , "Kept someone entertained" , "happily occupied" .)