I just got an unpaid internship at a law firm. It is somewhat helpful for what I want to do with my career but it was not my first choice. I have been there less then a week and when I applied the job description said the internship was a minimum of 3 months. Today I got an email from a government agency that is everything I need for my career. If I did not sign a contract and I am not paid, can I get in any serious trouble by quitting my internship early? Is it possible they would not let me leave?
This is general internship advice. I know nothing about law firms specifically.
It would generally be bad form, and the company may hold it against you.
But you're also an unpaid intern. Less than a week into said internship. If you quit gracefully then they probably won't hold it against you, and will have forgotten all about you within a couple of weeks.
If you quit tomorrow, it may even be early enough for them to offer a place to someone who didn't initially make the cut (assuming you went through some kind of selection process to get this internship in the first place).
Just make sure you actually have a job offer, contract-in-hand, from this agency before you quit.
I've seen more than a few questions about government hiring where the timespan between "we want to hire you" and actually arriving for your first day is longer than your entire internship would be.
Alternatively, they may be open to you starting in 11 weeks rather than today. It probably won't hurt to ask.