If your divorce decree or agreement provides that a either this specific significant other, or any significant other, may not have certain interaction with your daughter, either generally or under certain circumstances, that decree or agreement may be enforced.If the above is not the case, then IF you believe--and more importantly, can show--that either this person in particular or the way your ex intends to interact with significant others will cause emotional or pschological harm to your child--or even put her at some physical harm, then you may be able to go to court to get an order barring it. Be advised that this is a very high bar to get over: typically, you need something like inappropriate behavior (causual nudity), criminal behavior, mental illness, drug use, etc. to show this. That you and your ex are divorced and that he will have new people in his life is a fact of your daughter's life; as long as those people behavior in a reasonable fashion, it is very unlikely that a court would take any cognizane of it.