Is there a function that works exactly like the "Rotate 1D Array" function (can do both right and left shift directions), but simply places a zero value in place of new data? It's ok to lose the data that gets shifted out.
There is no single function that does this, but you can easily do this by using a combination of Rotate Array and Replace Array Subset. If you need this more than once, you can even make it a subVI.