Breaking up is hard to do. Whether you've been with your modeling agency for 5 months or 5 years, it's never easy to cut ties and explore other opportunities. But there may come a time when you feel the need to move on. Whatever your reasons, changing agencies is no small feat, and you need to ensure you're doing it for the right reasons and in the right way.

Good reasons to change modeling agencies
Your agency is no longer interested in you? Is your agent MIA? Have they stopped promoting your career? Are they no longer securing contracts for you? Of course, business may be slow, but your agency may have also stopped offering you work. If so, it's time to have a serious discussion with your agent to understand what's really going on.
Your agency doesn't have the right clients for your look. If you have a high fashion look but are signed with an agency that focuses on the commercial side of things, you won't get as many contracts as you'd like.
You no longer feel supported in your career goals. If your career plan doesn't align with what your agency has set for you, neither of you will be happy. However, before pulling the plug, make sure your goals are achievable (not all models are meant to become runway models, for example) and that your agency is aware of your plans.
You don't get along with your agent. You and your agent don't need to be best friends, but you should have an open, honest, and civilized professional relationship. If you're avoiding communication with your agent because you're scared or uncomfortable, it might be time to move on.
The agency has a bad reputation. No model wants to be associated with an unprofessional organization known for losing models and clients.
A better opportunity has presented itself. If another agency has better clients, better agents, better pay, and better conditions, then signing with them might be what your career needs. But don't rush and don't let your emotions guide you. Before signing with any agency, no matter how great it seems, you need to do your homework and conduct thorough research.

Bad reasons to change modeling agencies
You'd rather be signed with a big agency... just because. Remember that bigger isn't always better. While being on the roster of an elite agency may confer some prestige, it doesn't guarantee work. You'll be a small fish in a big pond of models, which means a lot of competition and less personal attention. It's not always the best environment for a thriving modeling career. Consider sticking with your smaller agency, unless, of course, it makes sense for you to level up.
You're upset/unhappy but haven't tried to solve the problem. It's entirely normal to want to change agencies, but you should a) make sure your agency is aware of your concerns and b) try to resolve issues together before storming out. The situation may be salvageable with some work and/or a change in direction. If not, or if your agent isn't meeting your needs, at least you will have tried!

When you're ready to change agencies
If you've communicated your concerns to your agent, done your best to address the issue, and are ready to sign with a new modeling agency, you still need to think about a few things before officially parting ways:

Legal aspects. First and foremost, you need to read your modeling contract. Many contracts require models to give at least 30 days' notice (sometimes more) to terminate the agreement, and some have "outs" that allow you to end it if the agency hasn't fulfilled certain obligations (like booking a certain amount of work, for example). If you leave before properly terminating your contract, you could face serious legal consequences, including financial penalties. Sometimes, the agency may not care much about your departure (don't take it personally) and doesn't mention the contract at all. If that's the case, you should still ask the agency or an attorney to draft a termination agreement, just to cover your bases.
Seek a second opinion. Whether it's from a lawyer or an experienced modeling agent, getting a second opinion can be very helpful.
Don't burn bridges. The modeling industry may seem vast, but in reality, it's incredibly small, and there's a good chance you'll encounter your agent or professionals associated with them at some point in your career. So, it's important to leave your agency on the best terms possible. Break up with them in person if you can (Skype is a good backup plan), kindly explain your reasons, thank them for everything they've done, and wish them good luck. And never speak ill of them to other models, agents, or industry professionals. Your harsh words may come back to haunt you and can significantly harm your reputation as a professional model.