"In general relativity and other relativistic theories of gravity, space and time are combined to form ``space-time'' which is curved in the presence of mass. As masses move, for instance like the two components in a binary system, ripples in space-time are created that propagate through the Universe, very much like waves caused by a stone falling into a pond. These ``gravitational waves'' (GWs) are known to exist from the effect that they have on a system of two orbiting stars. After inferring their existence indirectly, the next great challenge is the {\em direct} detection of GWs. While this is the aim of a number of gravitational wave detectors around the world, a detection has not been made. Fortunately, a method exists that allows us today to detect GWs directly, in a frequency range that is much lower but complementary to those covered by ground-based detectors. This method utilises the radio astronomical observations of a special type of star known as radio pulsars. We propose an experiment to achieve the ground-breaking goal of GW detection with the help of an innovative approach. At the heart of this approach, named LEAP, lies the goal to combine the collective power of Europe's biggest radio-telescopes to form the biggest fully-steerable telescope on Earth, providing a ``leap'' in our sensitivity to go beyond the threshold that delivers the first direct detection of GWs. While the rewards for a successful detection of GWs are immense, we demonstrate that this is possible by harvesting the experience and resources uniquely available in Europe."