Of course it depends on the circumstances. If you're on your own trying to maintain a test suite on the code of 50 other people, none of whom work on these tests and think you're just trying to slow them down for no good reason, there's no way that will work. But if there's only a few people working on the code and you can maintain tests for a more or less well defined part of it - it's possible (if you're experienced enough; if you have to spend 2 weeks reading up on how to do unit testing, it's not a viable strategy of course.)
Damn that's motivating. I'll be quoting you on this one.
If moving is not an option, then follow the parent's advice. Add all the missing tests as fast as you can. Explain what you are doing to your manager. And set up CI to email your team whenever anyone checks in breaking changes. This will motivate your teammate to start running your tests. If they are particularly narrow-minded, they will be unhappy about this. If this happens, reconsider your decision to stay.
Even after you write a lot of tests, coverage will be low. You will likely code some bugs that negatively impact the business. I urge you to find a mentor inside the company, a senior engineer or engineering manager, and show them code and explain the technical debt to them. Try not to blame your teammate for the situation, just explain to your mentor that you are concerned about introducing bugs. Ask them to keep your discussion confidential. Your mentor can back you up when your bugs negatively impact the business.
Definitely: this will help you to better understand what the code does and the dependencies involved. Climb up the dependencies tree and add tests there as well.
Do not be tempted into 'rewrites' because you're setting yourself up for failure.
It's a long play, yes. If you're feeling the way you describe just from the current state, you're probably not senior enough to do it. It requires much more than just technical skills - those are abundant, it's not what you can build a career on. It's a bit Machiavellan, I guess, but in the end, everyone wins - but you need to have the Vision that others are not able to understand, so you have to find ways to make it happen anyway, in adversarial circumstances.
Good luck.