Hi and Welcome to the Community Forum @Anonymous
If your original SIM card is a different sized one from the SIM card your new Phone takes then you need to either do the sim swap via the link ,Or text SWAP to 20220, or pop into your O2 store where they will do it for you.
This process takes from a few minutes to approx 24 hours to complete ,and your services return.
The service on your original sim will stop first ,and then your new SIM card will start to work.
Turning your phone off and on helps this process.
Or you can pick up a free sim adapter from an O2 shop in order to make your sim the right size if applicable.
If your new phone takes the same sized SIM card then it should work fine.
Ring Cs on 202 to have your account checked over.
Take care.