If you'd like to use it with linked records, lookups etc, I'm afraid the only way to do it is to copy/sync it to your other base

Alternatively, you could try automations with API calls in your other base to grab the data in your zip codes table?

Sure, you can communicate between bases by tapping into Airtable’s API.

This can be done in at least 3 different ways:

1. High-code: Write your own custom Javascripts.

2. Medium-code: Use the DataFetcher extension.

3. No-code: Use Make’s advanced automations for Airtable.

Hope this helps! If you’d like to hire an expert Airtable consultant to help you with anything Airtable-related, please feel free to contact me through my website: Airtable consultant — ScottWorld 

there may be other ways depending on your use case.  For example, you have a single zip code in base A and want Base B to return the city and state.  Create a sync from a to b with just the one record you want to lookup and empty city and state fields. When the record syncs to base b have base b update the state and city fields. 

That's a great suggestion from @Dan_Montoya.

Note that this would require two-way syncing, which requires being on a business plan or an enterprise plan.

You could probably get it to work with one-way syncing as well, but that would require a much more convoluted setup.

I would suggest using the new Airtable AI feature to look up zip codes, especially if a couple of mistakes wouldn't be system critical. - Brian