I was mentored and mentored other testers at work, working on real projects. It was basically about what to in a given situation that happens at work or how to solve a given technical problem.
Do mentors outside of work exist?
How they work if there's not real project at hand to talk about or check?
Yes, It is possible to find mentors outside of work place even for testing. Well maybe you wont have actual project as you do at the work place, but you can always come up with scenarios and work around them. Get your students to think and come up with scenarios or you define a few for them and then build up your training sessions accordingly.
OR
You can take open source projects from sites like sourceforge and work with them.
You can create ideas about how you can define and execute the course depending on your students' abilities. They'll be good in various areas. Some will be interested in testing the UI and user's end of the functionality, while others may be interested in security and so on. So you have to figure out what your students are good at and then build the course to help them improve their skills.
Short answer: Yes, it is possible. Mentorship outside of your job tends to happen in a more social context, though, and may provide some different benefits.
Mentorship outside of your job is more likely to be cross-disciplinary, cross-industry, mutual, non-explicit, and casual. You may have already have mentors in your family and your friends, or in old coworkers whom you have stayed in touch with. Anyone with whom you discuss your career, projects, or professional relationships may already be mentoring you, and you them. You may be able to get what you are looking for just by investing more intentionally in what you already have.
If intentionally growing existing relationships doesn't seem like the way to go, think about what you are seeking from a mentor, and see if that gives ideas.
If you want coaching, you may want to consider paying for a career coach - or ask a friend to be a "career growth partner", and meet for coffee or dinner and share successes, challenges, and planned next steps. You could also consider looking for training.
If you want to grow leadership abilities by mentoring, consider volunteer work where you are in a teaching or training role and see if any of your students are looking for a mentor in you as well as a teacher.
If you want sponsorship, look for programs designed to support people looking to take that next step in their careers.
If you want support and encouragement, or if you just generally want to grow your mentorship relationships without specifics, try professional networking events. Most cities with a healthy tech industry also have tech meet-ups and organizations that can provide opportunities to build relationships.
Basically, if you can define what you want, you can narrow your search. Remember that "mentorship" is just an aspect of a relationship, and it can grow out of almost any relationship; but do target your actions to those places most likely to provide relationships that grow the kinds of mentorship opportunities you are hoping for.
