What is most important is your seed phrase, if you have your seed phrase you your coins. You have setup Ledger Live one your new device, you have access to your coins, you spend from it, then you can delete the old wallet. But just as I have meant, it is not the new device that that you have your Ledger Live that is most important, what that is most important is your seed phrase offline backup, which you can use at anytime to recover your coins.