Updating a column in Table A from a Column in Table B during an after insert Trigger
You need a before insert trigger ("after insert", the bird has flown, it's useless modifying the new vales - if MySQL allows you).  In the trigger body, use the following code:

Declare v_tax int;
select tr.tax_combined_rate into v_tax from sales_tax_rate as tr
  where NEW.res_zip = tr.zip_code;
set NEW.res_sales_tax = v_tax;


See the effect here: https://www.db-fiddle.com/f/eEiK6pKGEQEoYL9BPdfooP/0