Instigated raunchy frolic in private with Duke (8)
I believe the answer is:
prompted
'instigated' is the definition.
('prompt' can be a synonym of 'instigate')
'raunchy frolic in private with duke' is the wordplay.
'raunchy frolic' becomes 'romp' (synonyms. I am not sure about the 'raunchy' bit.).
'in' is an insertion indicator.
'private' becomes 'pte'.
'with' says to put letters next to each other.
'duke' becomes 'd' (abbreviation).
'romp' going within 'pte' is 'prompte'.
'prompte'+'d'='PROMPTED'
Can you help me to learn more?
(Other definitions for prompted that I've seen before include "Given help with speech" , "Instigated" .)