  Guided us by the scenario of weak scale naturalness and the possible
existence of exotic resonances, we have explored in a $SO(5)$ Composite Higgs
set-up the interplay among three matter sectors: elementary, top partners and
vector resonances. We parametrise it through explicit interactions of spin-1
$SO(4)$-resonances, coupled to the $SO(5)$-invariant fermionic currents and
tensors presented in this work. Such invariants are built upon the Standard
Model fermion sector as well as top partners sourced by the unbroken $SO(4)$.
The mass scales entailed by the top partner and vector resonance sectors will
control the low energy effects emerging from our interplaying model. Its
phenomenological impact and parameter spaces have been considered via
flavour-dijet processes and electric dipole moments bounds. Finally, the
strength of the Nambu-Goldstone symmetry breaking and the extra couplings
implied by the top partner mass scales are measured in accordance with expected
estimations.
