Accepting your children being around their daddy’s new woman

How to learn to accept your children being around their daddy’s girlfriend/ new partner. Me and my children’s father have an understanding that we won’t be introducing anybody to our kids until we know it’s serious and potential. Looks like my kids’ father has been dating this new woman for a while and they are serious and potential in the long run. He said he wants the kids to meet her, for the first time after so much woman he has dated after our divorce and finally met his the one, how can I learn to accept and understand this new lady would be a part of my kids life? How to stay cool about it? Calling all moms who been in this situation.