Yes, it's possible, you do!

If you are transferring to plan.com from the O2 network and you have agreed with your account managers, the business you have been negotiating the contract with that you can retain your existing SIM card, then in those circumstances, your account managers will provide us with all the detail we require and a new SIM will not be required. 

In any case, if you've been supplied a new phone to go with your new plan.com contract, you may need a new SIM card as the SIM sizes can differ from manufacturer to manufacturer.

Discuss your needs with your account managers who sold the contract to you.