Duke learning about city once besieged (9)
I believe the answer is:
leningrad
'city once besieged' is the definition.
(Leningrad was besieged in World War II)
'duke learning about' is the wordplay.
'duke' becomes 'd' (abbreviation).
'about' indicates anagramming the letters.
'd'+'learning'='dlearning'
'dlearning' anagrammed gives 'LENINGRAD'.
(Other definitions for leningrad that I've seen before include "St Petersburg, 1924-91" , "Former name of city" , "old city" , "St Petersburg formerly" , "St Petersburg before nineteen ninety one" .)