You can automatically look up postcodes (zip codes) using a third party system called Loqate (formerly PCA)
To do this first of all you need to create an account and subscibe with the lookup provider: https://www.loqate.com/
Then configure Loqate in Settings->Integrations->Loqate:
And copy the API key found on your Loqate account page to BRM / RSM.
Once that is configured a Address Lookup box will appear on the customer detail page creating new or editing existing customer accounts: