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A large fraction of galactic nuclei is expected to host supermassive blackhole binaries (BHB), likely formed during the early phase of galaxies assemblyand merging. In this paper, we use a large set of state-of-art numerical modelsto investigate the interplay between a BHB and a massive star cluster (GCs)driven toward the galactic centre by dynamical friction. Varying the BHB massand mass ratio and the GC orbit, we show that the reciprocal feedback exertedbetween GCs and the BHB shapes their global properties. We show that, atGC-to-BHB mass ratios above 0.1, the GC affects notably the BHB orbitalevolution, possibly boosting its coalescence. This effect is maximized if theGC moves on a retrograde orbit, and for a non-equal mass BHB. We show that theGC debris dispersed around the galactic nucleus can lead to the formation of anuclear cluster, depending on the BHB tidal field, and that the distribution ofcompact remnants resulting from the GC disruption can carry information aboutthe BHB orbital properties. We find that red giant stars delivered by thespiralling GC can be disrupted at a rate of $\simeq (0.7-7)\times 10^{-7}$yr$^{-1}$ for BHB masses $\sim 10^7{\rm M}_\odot$, while tens to hundreds ofstars can be possibly observed in the galactic halo as high-velocity stars,with velocities up to $\sim 2000$ km s$^{-1}$, depending on the BHB orbitalproperties.

Supermassive black holes coalescence mediated by massive perturbers: implications for gravitational waves emission and nuclear cluster formation