Automatically calculate a "previous value" based on current slicer selection

Thanks for lbendlin's concern about this issue.

Hi, RYRY 

Since you did not give me some test data to test, I assumed some data myself:

DIM_Applicant:

DIM_day:

I will provide some steps below which I hope will help you:
First, create a calculated column in the DIM_day table:

Previous Day of Week = 
SWITCH(
    'DIM_Day'[day_of_week],
    "Monday", "Sunday",
    "Tuesday", "Monday",
    "Wednesday", "Tuesday",
    "Thursday", "Wednesday",
    "Friday", "Thursday",
    "Saturday", "Friday",
    "Sunday", "Saturday"
)

Then create the following three Measure in order:

Selected Day = SELECTEDVALUE('DIM_Day'[day_of_week])

Previous Day = 
CALCULATE(
    MAX('DIM_Day'[Previous Day of Week]),
    FILTER(
        DIM_Day,
        'DIM_Day'[day_of_week] = [Selected Day]
    )
)

Submitted Applications Previous Day = 
CALCULATE(
    COUNT(DIM_Applicant[app_id]),
    'DIM_Applicant'[app_status] = "Active",
    FILTER(
        ALL(DIM_Applicant),
        DIM_Applicant[day_submitted] = [Previous Day]
    )
)

Select Card visual and drag Measure Submitted Applications Previous Day into Card visual:

I have attached the pbix file for this example below, I hope it helps!

I hope my suggestions give you good ideas, if you have any more questions, please clarify in a follow-up reply.
Best Regards,
Fen Ling,
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