Yes you can do a SIM swap.
SIM swap allows you to transfer your mobile account (including phone number, credit and existing bundles) to a brand new SIM card.
When you swap SIMs there will be a short delay before the new SIM card is up and running, so it’s best to pick a time when you don't anticipate needing to use your phone urgently. You can also only do a SIM swap between 4:30am and 9:30pm.
Once you've received your new SIM, logout of your giffgaff account and go to this page: