As a Mono in a Poly relationship, I don't know if there's a way you can avoid the shock/hurt/etc., but talking about it before you develop another relationship can help keep the focus in the right place... then it's about you and your needs/wants/desires, and not about "someone else trying to take you away" from them. It's easy to blame the other person in that case and not focus on the real issue, which is what you need.
If you truly do believe it is a piece of you, then I would recommend that even if your partner has a hard time dealing with it, don't hide it in a cave thinking that they'll "come around" eventually. It's easy for them to believe that if you can hide it, it's not important to you, and you'll have an uphill battle to fight later.
Good luck to the both of you. It's not easy to talk about it, but talking sets the foundation for all the communication you'll need to have in the future.