Is your data has any associated date/time value column?
Assuming that an individual Client Name could not have two different Client Tier values (say John Tier is 1 as well as 2) at a particular time point.
And considering that the Client Tier is getting updated repeatedly, i believe there should be a time value (for e.g. daily, hourly, etc) when a Client Tier value is getting changed.
Using this date/time column we can display the last state of Client Tier for the complete time range, selected Time slice as well as for a particular time point, in the viz.
To achieve this, simply select the 'Transform your data to enable Timeseries analysis' checkbox in the Designer data table.
Add the Client Name column to the Breakdown and the Client Tier column to the Visual Members variable of a Table viz.
Now, the table viz should be displaying the last state of Client Tier for the complete time range.
Add a Time Filter to the dashboard, to view the last state of Client Tier for a particular time slice.
Use the Snapshot handle on the Time Filter, to view the last state of Client Tier at a particular time point.
Hope you find this helpful.