In the event you have a ceramic-disk black and copper kitchen tap, a worn-out O-ring may be the source of the problem. In this case, it is possible to replace the spout with a new one. You can remove the handle by pulling up on the spout, but you may need to remove the handle and other parts first. If you can't remove the O-ring, you should get a replacement kit. You can also use plumber's grease on the handle.