Clusters of galaxies — with their turbulent magnetic fields and abundant matter content — are a promising class of potential neutrino sources. Cosmic rays accelerated within the large-scale shocks, Active Galactic Nuclei (AGN), or both can be confined in galaxy clusters over cosmological timescales and produce a steady flux of neutrinos in secondary interactions. The IceCube Neutrino Observatory has detected a diffuse flux of high-energy astrophysical neutrinos. After ten years of operations, however, the origin of this flux remains largely unconstrained. In this work, we perform a stacked search for neutrinos, using a population of over one thousand galaxy clusters detected by the Planck Satellite via the Sunyaev-Zeldovich (SZ) effect up to a redshift $z = 1$. We present the first results on the contribution of galaxy clusters to the diffuse neutrino flux and discuss the implications for various models of cosmic-ray acceleration in large-scale structures.