No, hardly anything is stored on the sim at all.
You need to backup your iPhone 4 to iCloud and then reinstall that backup onto your 5c.
It will ask when you set up the 5c if you want to set up as new or restore from backup, so choose the restore option and sign in to iCloud.
Wait whilst it completes then you'll need a sim swap at an o2 shop to change from a micro to a nano sim.
They will do that for free for you too.
I have no affiliation whatsoever with O2 or any subsidiary companies. Comments posted are entirely of my own opinion. This is not Customer Service so we are unable to help with account specific issues.
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