AppleCare coverage after screen replacement on a broken iPhone

Your AppleCare duration won’t be affected as long as your screen replacement is done by Apple or an Authorized Apple Service Center.

Let's clarify what you mean when you say that your screen is "broken".

If the screen was "broken" as a result of physical damage, the repairs will not be covered under the normal AppleCare warranty unless you have purchased optional AppleCare+ coverage.

If the screen is "broken" as a result of a manufacturing defect, then the regular AppleCare coverage would cover the cost of repairs.

Can you provide more details on exactly how the screen was "broken"?