Drunk, with most of gin knocked back, I start to offend American likely to sue (9)
I believe the answer is:
litigious
'likely to sue' is the definition.
'drunk with most of gin knocked back i start to offend american' is the wordplay.
'drunk with' becomes 'lit' (I've seen this in other clues. I am not sure about the 'with' bit.**).
'most of' means to remove the last letter.
'knocked back' is a reversal indicator.
'start to' suggests taking the first letters.
'american' becomes 'us'.
The initial letter of 'offend' is 'o'.
'gin' with its last letter removed is 'gi'.
'gi' backwards is 'ig'.
'lit'+'ig'+'i'+'o'+'us'='LITIGIOUS'
(Other definitions for litigious that I've seen before include "keen to go to court" , "Disputatious" , "Keen to pursue lawsuits" , "Prone to sue" , "Fond of going to law" .)