We perform the first harmonic space joint analysis of Galaxy Clustering and Weak Lensing cosmological probes with the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) public data. This project has two main goals: (i) set precise constraints to ΛCDM cosmological parameters analysing the HSC-SSP public data in this multi-probe study and (ii) develop measurement and analysis tools that will be required when the Rubin Observatory Legacy Survey of Space and Time (LSST) starts operating at the end of 2023. HSC is optimal as a precursor of the LSST Dark Energy Science Collaboration (DESC) as it is the deepest Stage III survey and uses a prototype version of the Rubin Science Pipeline. One of the highlights of our process is that we apply mode deprojection as a method to correct for the impact of observing conditions in the galaxy density field and in the spin-2 shear field. Another important ingredient in a multi-experiment analysis is the covariance matrix, necessary to account for the correlation between the different probes. We describe the implementation of the Gaussian and Super-Sampling terms. As our main result, we present preliminary constraints in the plane Ωm – S8 that are competitive with the current state of the art.