Just because you split from your old riding instructor doesn't mean you can't go back to her for a brush up or riding help. That will make him/her feel special and help you improve on your riding. You may also consider staying with him/her longer. A new instructor can be a good and bad change. Good luck!
Before making the decision to move, I think a conversation with the current instructor is order. Make sure that you have some clear goals that you want to achieve, not just to "keep progressing." Write them down then discuss them with your current instructor. With clear goals, she might be able to help you achieve these. She might also recommend that you go to another instructor, and could offer suggestions. Switching to another instructor without being familiar with them is a big gamble. Clinics with other trainers might also be a good idea to check out. Just keep the lines of communication open. So many problems can be avoided by communicating. Best of luck!
There are a lot of considerations that need to be made before this question can be answered well. You said you have been with the same trainer since you were a beginner, how many hours have you had in the saddle? Someone can ride for years, but if they do it infrequently (casually lesson/ride ~once a week), the solid foundation you need to establish before moving on to more advanced movements may just not be there yet. Riding takes a lot of practice and working on the same things over and over to get them right, not only for your safely, but for your horse as well. If you are riding infrequently are upset with lack of progress you might help yourself get better by talking to your instructor about leasing options (or buying) so you can practice more outside your lessons. If you feel like you are losing sight of your goal you can do the simplest thing ever and just ask! Maybe something with your balance or timing just isn’t quite right and you need to work on developing a better “feel”. Make sure you are actively listening during lessons. If your instructor seems to be giving you the same advice over and over again, it might not be them. Ask someone to video your ride and watch it later analyzing yourself critically. Are you really doing everything they are asking of you or glossing over the finer details saying, that’s good enough? Good enough is never enough and that mentality won’t get you very far. If you truly want to improve and learn new skills be HONEST in your critique. Another simple solution is to ask your trainer if you (and your horse) are ready to try something new or different. Sometimes what you work on in lessons has to do with your horse as well. If you have aspirations to jump 5’ fences and doesn't have the scope, that might be an issue. Or if you have a green horse, it takes time and work to get your horse where you want them to be. You and your horse have a partnership and you both have to be physically and mentally ready to tackle new experiences. That being said, if you have made it this far, spent more hours in the saddle then sleeping, spoken to your instructor about what you need to work on, have watched yourself ride, know your horse’s physical and mental capabilities and your own and you are still not satisfied, maybe it is time to make a switch. Again, not knowing which discipline you are speaking of I can only guess at this, but in a generalized way: if you have covered the basics of w/t/c and have good communication with your horse and want to start specializing in a discipline that your trainer is not an expert in, there shouldn’t be any hard feelings. The most important thing is to talk to your trainer about your goals and the steps you need to take to get there. Lastly: NEVER feel discouraged. Everyone hits plateaus no matter what their discipline or riding level. All you can do is work hard and be the best horse person (therefore best learner) you can be. Hope this helps!
I had a very similar situation. I took western lessons at a barn for 2+ years. My instructor was awesome and super fun, but after awhile it seemed like, as you said, supervised practice. I also wanted to start a different discipline (branch out a little), so I switched to a jumping instructor. My trainer totally understood and we are still great friends. There's nothing wrong with paying your previous instructor a visit to say thanks for their awesome help!
If you have a good relationship with your instructor then you should be able to talk to him/her about your situation without offending them. Be honest but grateful about all the help you've received in the past.
Be honest and extremely grateful. Hopefully your instructor will understand and offer to be there for you on your journey. Send her updates on your progress if she is open to continuing a relationship. If not, no worries - you need to do what is best for you and are not responsible for how she handles the news. Your responsibility is to share it with as much grace and thankfulness for where she has brought you to be able to move to the next level and without her, you would not be where you are today - Huge Thank You!
Look around, watch, and do your research. I was with an instructor that, for a long time, didn't teach me a single thing. I quit with her and months later, my sister did as well. We switched to a new barn where we've been for over a year and we LOVE it! Neither of us has ever had our own horse, but the school horses are great and everyone at the barn is as well. Every trainer–even the sub trainers–are awesome. They're all accomplished and tailor their instruction to who they're teaching, paying attention to what the riders want and need to learn. I've learned more there than I did in my 8-9 years at other barns. All the others were worthless compared to Spring Run. I can only imagine where I'd be if I had started out here. Follow your heart and what your instinct tells you is right. Don't stay somewhere where you're miserable. Riding should be enjoyable. If it's not, someone's doing something wrong.
As an instructor myself, I understand when someone feels they will grow under a new person. I teach beginners and up but I don't expect to take one person all the way. Having different teachers is good for most riders at different points in their riding career. What I don't like is having a student say they are taking a break and then a month later see pictures on social media of them riding somewhere else. Just tell me, I will understand.
If your instructor truly understands the horse world and the direction that you are trying to go by taking lessons you can just say it point blank. Explain to them that, although you have really enjoyed your time learning from them and would like to be able to ride with them on a more personal level, you feel it would benefit you more to move on to an advanced trainer. To make them feel better about you moving on to a new trainer you could ask their opinion on some potential trainers and even ask if they have anyone they would recommend. This way they feel that you truly do trust their opinion and you will still feel that you can ask them for advice even when they aren't your trainer. Hopefully your trainer will understand your feelings and can still stay in your life as a friend and possibly a riding buddy.