I’m involved with a married woman who also wants freedom to date other men. Her spouse already approves of me, but what am I risking here? I've been her other partner for 7 years. Are there conditions that we also must have?
To answer your questions, you are not “risking” anything, and there are no “conditions” that you “must have.” This woman is clearly very capable of maintaining happy, healthy, non-monogamous relationships - she’s been in one with you for seven years! Whatever arrangement exists between you, her, and her husband is clearly working. You don’t need to set new conditions arbitrarily, because they aren’t really needed.
It sounds like you’re worried this will fundamentally change your place in her life, but I’d encourage you to think about why that is. You may feel like each “established” male partner needs to approve of the next new guy - her husband let her date you, now you get to set the terms for her dating someone else. That’s not how it works! She is dating non-monogamously, and that includes you, but as an independent, individual person, her dating life is centered on her, not on you.
Think about what has made things work so well with you, her, and her husband; and how you two can maintain those relationship practices as she dates other people. Think about whether you pose a “risk” to her husband. Hint: you don’t, and you have seven years of evidence to back that up! Relax, let go of zero-sum or possessive-type relationship framings, and support her!