An upgrade, by definition, is a change of either equipment and/or payment plan whilst retaining your number as a matter of course. If you have a physical SIM, then an upgrade phone is supplied and you simply move your existing working SIM from your old phone to a new phone.
As regards the finance, the answer depends on which plan you have. EE's traditional contracts have no concept of paying off a device - you have one single monthly fee covering all your airtime and device repayments, which you agree to pay for at least the duration of your minimum term. Once that minimum-term has completed, you are free to choose one of several options, one of which is to change your plan to a SIM-only.
EE's newer FlexPay plans are structured as two independent & separate contracts. You have a fixed-term finance loan for your device repayments and once that loan is repaid, the contract naturally ceases. You then have a standard 30day-notice airtime plan with a minimum-term - in a similar way to an 18/24month SIM-only plan. Once the minimum-term is complete, the exact same choices are available to you as with any other plan.
