Eliot admits the greatest lunatic is working like a charm (10)
I believe the answer is:
talismanic
'like a charm' is the definition.
(I've seen this before)
'eliot admits the greatest lunatic' is the wordplay.
'eliot' becomes 'ts' (TS Eliot).
'admits' means one lot of letters goes inside another.
'the greatest' becomes 'ali' (film about Muhammad Ali).
'lunatic' becomes 'manic' (I am not sure about this - if you are sure you should believe this answer much more).
'ts' enclosing 'ali' is 'talis'.
'talis'+'manic'='TALISMANIC'
'is working' acts as a link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Another definition for talismanic that I've seen is " like a charm".)