The two lists
Here I've pasted in my two lists.
The Allowed list is the list of APIs currently allowed for System X to call.
The Required list is the list of APIs System X's new function requires.
The question is, which of the required APIs need to be newly allowed?
Specify Duplicate Values formatting
Select the two lists of cells. Here they are contiguous, so I just selected the whole range. But if your columns are apart on the sheet, you can select non-contiguous ranges.
On the Home ribbon, select Conditional Formatting > Highlight Cells Rules > Duplicate Values...
Specify type and format
By default, the first setting is Duplicate. Change this to Unique and then change the highlighting colours if desired. You can already see the results. Click OK.
That's it! Deselect the range by clicking in another cell to more easily see the results.
Those cells highlighted in red are unique within the cells that were selected. Assuming no duplicates within either of the lists, then the result is that those highlighted in one list are not present in the other.
Now we know that the highlighted cells in the Required list are the APIs that will need to be added to the Allowed list (in real life).