If im recycling my very old iMac do i have to reinstall the O S?

Apple advises that you erase your personal data from your devices before you send them in for recycling, but they do also state that they will erase your personal data during the recycling process if you haven't:

Your personal information will be completely wiped from your device, so make sure to back up your data before you send it in.

Recycling - Apple (ME)

Apologies for misunderstanding your question! You don't have to reinstall the operating system.