Your React client will run in development mode - when you want to deploy to a live server, you will need to build the front-end and serve the static files.
// build the client
cd client && npm run build
You can run this file before you deploy, or set it as a post build script in package.json if your hosting provider supports post build scripts.
Gravity will automatically serve the static files from the server when running in a production environment.

Environment Variables

You will need to ensure you set up your environment variables in your production environment.

Heroku Deployment Tutorial