Cunning Italian author entertains duke in style (3,4)
I believe the answer is:
art deco
'style' is the definition.
(decorative style)
'cunning italian author entertains duke' is the wordplay.
'cunning' becomes 'art' (I've seen this in another clue).
'italian author' becomes 'eco' (Umberto Eco).
'entertains' means one lot of letters goes inside another.
'duke' becomes 'd' (abbreviation).
'art'+'eco'='arteco'
'arteco' going around 'd' is 'ART DECO'.
'in' is the link.
(Other definitions for art deco that I've seen before include "1920s and 1930s ornamental style" , "Redcoat (anag) -- inter-war design style" , "Geometric style of ornamentation" , "Old style" , "1920s and 30s style of art and architecture" .)