Something very cold about lord close to you, dictator (2,4)
I believe the answer is:
il duce
'dictator' is the definition.
(Il Duce is an example)
'something very cold about lord close to you' is the wordplay.
'something very cold' becomes 'ice'.
'about' is an insertion indicator.
'lord' becomes 'ld' (abbreviation for the aristocratic title).
'close to' says to take the final letters (the close/ending of).
The final letter of 'you' is 'u'.
'ld'+'u'='ldu'
'ice' going around 'ldu' is 'IL DUCE'.
(Other definitions for il duce that I've seen before include "Italian leader" , "Name for Fascist" .)