A goddess duke entertained (6)

I believe the answer is:

amused

'entertained' is the definition.
(amusing is a kind of entertaining)

'a goddess duke' is the wordplay.
'goddess' becomes 'muse' (I've seen this in other clues).
'duke' becomes 'd'.
'a'+'muse'+'d'='AMUSED'

(Other definitions for amused that I've seen before include "Made (someone) laugh" , "Delighted" , "Provoked mirth in" , "Tickled pink" , "Queen Victoria wasn't!" .)

I've seen this clue in The Telegraph.

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