Can I clip a part of a basemap on ArcMap 10.4?
I'd like to know if it is possible to clip a basemap, specifically OpenStreetMap.
I suppose you mean extracting an image from a basemap raster (flux). You can add your basemap, then go to File/Export Map...
In the dialog box, set the dpi you need, and for example for JPG files, don't forget to check the "Write World File" box. Then you insert your exported image.
Next step if you really need to CLIP by for example a polygone boundary, is to use the Extract By Mask Tool on your new image (you will need Spatial analyst Extension for this last part).