When creating a new account, Game Center/Play Services will automatically be added to your account
Go to the Settings screen, there will be a "Connect"-button with a Game Center/Play Services icon. Press it to start connecting your account to Game Center/Play Services. If you already have connected to another account, then you will be prompted if you want to move the connection from an older account, to the current one. If the button doesn't appear in the settings screen, try closing the app and starting it again.