Symbol of power not concerning one cold philosopher (7)
I believe the answer is:
Here is my best explanation:
'philosopher' is the definition.
(sceptic is a type of philosopher)
'symbol of power not concerning one cold' is the subsidiary indication.
'symbol of power' becomes 'sceptre'.
'not' suggests deleting specific letters.
'concerning' becomes 're'.
'one' becomes 'i' (roman numeral).
'cold' becomes 'c' (eg on taps).
'sceptre' with 're' taken away is 'scept'.
(Other definitions for sceptic that I've seen before include "Agnostic", "Doubter; atheist", "A doubting Thomas", "He's hard to convince", "One habitually doubts accepted beliefs", "One inclined to question accepted opinions", "Person who tends to disbelieve", "Someone inclined to disbelieve", "One questioning accepted opinions" and "One who doubts the truth of religions".)