Unfortunately, PS4 does not allow other apps to import captures directly at this time.
However, you can still import PS4 captures if you upload them to another service such as Facebook or Twitter first. Once uploaded, select Facebook or Twitter from the importer menu to select your capture.
If you don't want your Facebook friends to see your unedited PS4 captures, you can set the privacy setting to Only me when uploading them to Facebook. They will still be available in the Clutch importer.