Although trapping and manipulation of small objects have been of interest for a range of applications and many clever techniques have been devised, new methods are still in great demand for handling different materials and geometries. Here, we report on an electrostatic trap that is created in an aqueous medium between the aperture of a nanopipette and a glass substrate without the need for external potentials. After a thorough characterization of the trapping conditions, we show that we can displace or release a particle at will. Furthermore, we demonstrate trapping and manipulation of nanoparticles and lipid vesicles attached to lipid bilayers, paving the way for controlled studies of forces and diffusion associated with biological membranes. We expect the technique to find interesting applications also in other areas such as optonanofluidics and plasmonics.