I would wait a while & try switching your phone off then on again.
Follow the instructions on the card attached to the new SIM & wait up to 24 hours (usually 30 minutes).
Switch the phone on & off a couple of times.
When activated you should see Giffgaff in the top left hand corner of your phones screen.
If you still have a problem look at the following link:https://support2.giffgaff.com/app/ask/Getting-Started/Activating-my-SIM/form/