The installation of the application needs to be done by the account with the required permissions. It can be the Owner of your LiveChat license or one of Admins with Billing Permissions. Find the DeepL Translate integration in your LiveChat Marketplace and add it to the cart. Once the checkout is done you should be able to click the Install button in the top right corner of the integration page.
Once the installation is completed, go to your LiveChat agent application Settings, choose Manage Apps and click DeepL Translate to open its settings.