Hi! Here are two options. I am sure there are others.
If you have a recent version of Excel you can use Power Query (it is included in Excel) to grab the data you need from the other file and place it as a table on the invoice file. Then you can create your dropdown list with Data Validation referring to that table. When you create the query, you can set the properties to make it run every time the invoice file open, so that you get the most current version of the data.
Alternatively, you can create a sheet on the invoice file and put an array formula referring to the file where you have the client names. Array formulas as more difficult to break. In this case, you need to extend the formula to more cells than the ones you currently have to accommodate for new client names that might be added.
Open the two workbooks.
See pic 1 for the formula to write on the invoice workbook. (just type "=" and then click the first cell with the first client name on the other workbook.
Then, INSTEAD of Enter, click CTRL+SHIFT+ENTER so that the curly brackets appear.
Then extend the formula down as much as you need.
You can close the client database.
Now you can create the data validation based on your list in the invoice new sheet.
I hope this works.
Let me know if you need further help.