What will be the impact on existing tickets if we update some dropdown fields?

When you remove an item or option from the Dropdown field, this would automatically remove the value from the tickets and reports as well. The same happens when you rename or make any changes to the values of the field.

The process that needs to be followed would be to create a new value in the same Dropdown field and Bulk change the values in all the tickets that you need. Once this is done, you can remove the value from Admin > Workflows > Ticket fields.