Answer:
It's not ideal to run different virus guards at the same time as they can interfere with one another. If you want to delete the old anti-virus software, make sure you uninstall it properly, rather than just delete it from the machine. If you really want to have both, you should disable the one that's already on the machine before installing the new one. Once you've installed the new one, you can reactivate the old one. Depending on what you're using, you may have to add both anti-virus programmes to the other's list of trusted programmes.