Do I need to remove the SIM card from my erased iPad Air before handing it over to someone else

Yes, you need to remove the SIM card - as this relates to your Cellular data plan. Any associated billing and charges are yours - and yours alone.

If it still holds your active cellular service plan, then. yes, you should remove it.

If you have cancelled the plan, or migrated it to a new device, or the SIM card is not active anymore, then you can leave it inside.