Offensive old actor's admission repelled American (6)
I believe the answer is:
odious
'offensive' is the definition.
(I've seen this in another clue)
'old actor's admission repelled american' is the wordplay.
'old' becomes 'o' (abbreviation).
'actor's admission' becomes 'ido' (I can't justify this - if you can you should believe this answer much more).
'repelled' is a reversal indicator.
'american' becomes 'US' (United States).
'o'+'ido'='oido'
'oido' backwards is 'odio'.
'odio'+'us'='ODIOUS'
Can you help me to learn more?
(Other definitions for odious that I've seen before include "Really obnoxious, generally disliked" , "Abominable, detestable" , "Hateful, generally despised" , "Really hateful, detestable" , "Loathsome and repulsive" .)