Admired one's having nothing to do with a dictator? (4)

I believe the answer is:

idol

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'admired one's' is the definition.
(I've seen this in another clue)

I don't understand the remainder of the clue.

(Other definitions for idol that I've seen before include "Honoured figure" , "Personal hero" , "One much admired" , "Worshipped image; lido (anag.)" , "As before, fake" .)

I've seen this clue in The Times.

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