Before you have this conversation, make sure you thoroughly study up on no-contact and TRANSPARENCY. There's a huge difference between "honesty/faithfulness" and "transparency."
Honesty and faithfulness are the goals, the non-negotiable standards. Transparency is the "constitution" that governs the goals.
Think the difference between telling an alcoholic spouse "Well, I would need you to be sober," and telling them "The spouse that I recommit to will need to demonstrate their commitment to sobriety by entering themself into a formal "12-step" type program, and remaining 100% committed to it. Whether or not that's you, only you can decide, but it's an absolute deal-breaker for me."