[mioelnir]

As others have noted, there are interim letters that you can request without reason at any time. But, there are also events that allow you to request them due to that event. For example if your team lead switches jobs, you can request an interim letter due to that, and it will be noted that this is the reason for writing it.

Those do not tip your hand and you requesting them is considered absolutely reasonable - how would your new boss of 3 months write that letter for your entire employment? These are what you use while still employed.