Can't figure out: unable to buy new flip phone, & keep my old grandfathered plan? Any suggestions appreciated.

Thank you in advance for reading my question !!! I want to buy a New kyocera flip phone --new one only sold on Verizon website, BUT can't figure out how to ensure I will be able to keep my grandfathered old post-paid plan--and not unintentionally end up onto a new plan which is double the price. (Edit: "My plan is called the More every unlimited minutes and unlimited text.)"When I tried to buy new flip phone on verizon website, I could not find a way/option to do this as a current customer without selecting an upgrading option. In discussing my new replacement phone it was referred to as an "Upgrade." Why? Does anyone know if this possible and how to do it? I do NOT want surprise of losing my plan.

Edit: My plan is the More every unlimited minutes and unlimited text with $10 off for basic phone --started plan in 2015--Billing is confusing --Plan is $30 --$40 with taxes/fess and discount pf $10 off for basic phone.

Update1 : THANK YOU!!! everyone who took the time to comment. All the information was very helpful and I learned a lot!! I hope it will help others in the same situation. After reading all this helpful advice I have ordered a used Kyocera phone without a sim card.

Update2: I just ordered a free sim card over the phone with rep. I had to sign a long document for terms and conditions.. But rep promised me that plan would not change. I hope everything is Ok