How to unpair two phones

I just got a new phone and to make things easier I have transferred all the data from my old iPhone onto my new one. I gave my sister my old phone but for some reason every time I add new contacts on to my new phone they add on the old one too and when I delete it from the old phone it deletes from my new phone too, it’s like the phones are paired and whatever you do to one it happens to both. How can I stop this from happening? How do I unpair the two phones?