Royal title (4)
(Other definitions for duke that I've seen before include "High hereditary title in Britain" , "Highest ranked British peer" , "Nickname of John Wayne" , "- - Ellington (jazz musician)" , "Nobleman of the highest rank" .)
'royal title' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for sire that I've seen before include "Generator" , "Stallion; beget" , "Male parent of, say, horse" , "Rise for male parent (4)." , "Old form of address to king - rise to it" .)