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Abstract: Floquet engineering could induce complex collective behaviour and interesting synthetic gauge-field in quantum many-body systems through temporal modulation of system parameters by periodic drives. Using a Floquet drive on frequencies of the magnon modes, we realize a chiral state-transfer in a hybrid photon-magnon system. The time-reversal symmetry is broken in such a promising platform for coherent information processing. The cavity-photon mode is adiabatically eliminated in the large-detuning regime and the magnon modes under conditional longitudinal drives can be indirectly coupled to each other with a phase-modulated interaction. The effective Hamiltonian is then used to generate chiral currents in a circular loop, whose dynamics is evaluated to measure the symmetry of the system Hamiltonian. Beyond the dynamics in the manifold with a limited number of excitations, our protocol applies to the continuous-variable systems with arbitrary initial states. In addition, it is found to be robust against the systematic errors in the photon-magnon coupling strength and Kerr nonlinearity.