Store old data upon refresh?

I think you can try the 'Include in report refresh' option. This needs to be setup while you are creating the table.
1. Create/load a table1 (query) with historic data. 

2 .Create/load another table2 (query) with current data.
3. On table1 - rightclick - uncheck 'Include in report refresh'. Would advise uncheck 'Enable load', as table1 will only be used for append.

4. Append table1 & table2

Now each time you refresh table1 will not get refreshed & table2 will bring in new data.

It is not dynamic, which I also want an option, you may want to transfer table2 data manually at source for any data to be termed as historic.

'Include in report refresh' prevent refresh of table each time.
Read more here : https://learn.microsoft.com/en-us/power-bi/connect-data/refresh-include-in-report-refresh