Clue: American bangs me entering pub, initially taking offence (12)
Answer: INFRINGEMENT
Explanation: Definition: offence
 [ FRINGE(front section of one's hair hanging over and cut straight across the forehead, refered to in North America as "bangs") + ME ]**contained in**(entering) INN(a pub/establishment serving drinks mainly) + **1st letter of**(initially) "taking".