Offensive old actor's admission repelled American (6)
I believe the answer is:
odious
'offensive' is the definition.
(I've seen this before)
'old actor's admission repelled american' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'actor's admission' becomes 'ido' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'repelled' says the letters should be written in reverse.
'american' becomes 'US' (abbreviation for United States).
'o'+'ido'='oido'
'oido' written backwards gives '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" .)