Lover boy entertaining old city agency (6)
I believe the answer is:
bureau
'agency' is the definition.
('bureau' can be a synonym of 'agency')
'lover boy entertaining old city' is the wordplay.
'lover boy' becomes 'beau' (I've seen this before).
'entertaining' indicates putting letters inside.
'old city' becomes 'ur' (ancient city state).
'beau' placed around 'ur' is 'BUREAU'.
(Other definitions for bureau that I've seen before include "Agency - writing desk" , "Office; writing desk" , "Chest of drawers or office" , "The ------, familiar name of the FBI" , "The B in the FBI" .)