Something very cold about lord close to you, dictator (2,4)
I believe the answer is:
Here is my best explanation:
'dictator' is the definition.
(Il Duce is an example)
'something very cold about lord close to you' is the subsidiary indication.
'something very cold' becomes 'ice'.
'about' indicates putting letters inside.
'lord' becomes 'ld' (abbreviation for the aristocratic title).
'close to' says to take the final letters (the close/ending of).
The last letter of 'you' is 'u'.
'ice' placed around 'ldu' is 'ilduce'.
(Other definitions for il duce that I've seen before include "Italian leader" and "Name for Fascist".)