My question is how can I please my girlfriend again after a serious quarrel?
That’s a very vague question with TLI for me to know what that serious quarrel was about or how many times you’ve been having that same serious quarrel. Did you cheat, again? If that’s the “quarrel” then maybe you’ve run out of chances with her. Whatever happened, if you really want to try again, talk to her, say you’re sorry, beg, cry, promise her anything. If she forgives, don’t screw up again. If she won’t forgive, take it as a learning experience and don’t screw up when you’re in a new relationship. ~ Queenie