(Instructions are for Windows 10. They may differ slightly in older versions of Windows.)
When you uninstall Office 2013 (or an older version) and install Office 2016 from Office 365, you may find that Excel 2016 isn't the default to open Excel files. To restore it, first search for "Default Programs" and select that. Under "Set your default programs" search for "Excel 2016" and, if it appears, click on it and select "Set this program as default."
If Excel 2016 does not appear among the default programs, you need to find a path to it. Type "Excel" in the search bar, and right-click on the Excel 2016 icon in the search window. Select "Open file location" and copy down the path to Excel 2016.
Now, going back to "default programs," choose "Associate a file type or protocol with a program." This gives you a list of extensions and the program that opens each. The main extensions associated with Excel are .xls, .xlsx, .csv, sometimes .xlsm. Click one of these and and the "Change Program" to the upper right of the search window. Click "More Apps." If Excel 2016 appears, choose that. If it doesn't appear, click "Look for another app on this PC" and use the path you found in the previous paragraph to locate Excel 2016. Select it and click the close button. Once you choose Excel 2016 for one extension, it should appear as an option for other extensions.