If you install an eSIM into a device that already has a SIM card in it, then nothing happens to any existing services you have. The two cards can co-exist quite easily, but there are a handful of changes you’ll need to make.
First and foremost, you may need to configure your settings to designate one SIM as being the dominant one for texts and calls. This varies depending on your provider, however.
You will also need to make sure that neither SIM is interfering with the other regarding service.